CN1632830A - Automatic Segmentation of Cerebral Ischemic Lesions - Google Patents

Abstract

The invention relates to image processing technology, in particular to an automatic segmentation method for cerebral ischemic lesion areas based on multi-scale statistical classification and local volume classification methods. The method includes the following steps: (1) estimating the diffusion tensor and diffusion anisotropy of the DTI image; (2) calculating the scale space; (3) multi-scale statistical classification; (4) reclassifying local volume voxels. The method of the invention effectively overcomes the influence of noise, diffusion anisotropy, local volume effect and intensity inhomogeneity, and realizes automatic segmentation of cerebral ischemic lesion areas in DTI images. It has important application value in the fields of medical image aided diagnosis system, medical image three-dimensional reconstruction system, and clinical pathology qualitative and quantitative diagnosis analysis.

Description

Automatic Segmentation of Cerebral Ischemic Lesions

technical field

The invention relates to image processing technology, in particular to an automatic segmentation method for cerebral ischemic lesion areas based on multi-scale statistical classification and local volume classification methods.

Background technique

The so-called image segmentation refers to distinguishing different regions with special meaning in the image, these regions do not cross each other, and each region satisfies the consistency of a specific region. From the perspective of processing objects, segmentation is to determine the location of the target of interest in the image matrix. Obviously, only by extracting the "target object of interest" from the complex scene, can further quantitative analysis or identification of each sub-region be possible, and then the image can be understood. Image segmentation includes methods such as threshold segmentation, edge detection, and statistical classification. The features available for image segmentation include image grayscale, color, texture, local statistical features or spectral features, etc. The difference of these features can be used to distinguish different target objects in the image. Since we can only use some features in the image information to segment regions, various methods must have limitations and pertinence, and we can only choose appropriate segmentation methods according to the needs of various practical application fields.

Currently, one of the most important practical applications of image segmentation methods is the segmentation of medical images. Medical images include images obtained by CT, MR, and other medical imaging equipment. At present, most researches on medical image segmentation focus on MR images or take MR images as examples. The research on medical image segmentation methods has two notable features. One is the general use of medical domain knowledge, such as the general shape of the ventricle, the content and relative position of intracranial white matter and gray matter, etc., and the other is often used. The way of three-dimensional segmentation, because the general image only has two-dimensional data, that is, the two-dimensional projection of the three-dimensional scene through the camera or other imaging equipment, while the medical image directly gives the data in the form of two-dimensional slices. Organized 3D data, which provides the possibility for 3D segmentation. For medical images, there are many specific segmentation methods, such as region-based threshold segmentation, region growth and split merging, classifiers and clustering, and methods based on random fields; in addition, there are edge-based parallel differential operators, Surface fitting method, boundary curve fitting method, etc.

Among medical imaging methods, diffusion MRI is an important means of clinical diagnosis, especially for stroke diseases. Stroke is a very serious disease, which may lead to permanent disability and even death. Diffusion weighted magnetic resonance imaging (DWI) is a very important and effective clinical method for detecting cerebral ischemia. In particular, DWI can detect lesions in the acute stage of onset, which is unmatched by conventional MRI techniques. Accurate detection of the location and size of cerebral ischemic lesions is helpful for classifying diseases, estimating disease status, and guiding treatment. However, due to the influence of signals such as T2 weighting, rotational density, T1 weighting, and the direction of white matter fibers, the contrast of DWI images is very low; and only using DWI images cannot provide sufficient diffusion information. Therefore, in clinical practice, diffusion tensor magnetic resonance imaging (DTI) technology is increasingly used to quantitatively estimate and analyze the diffusion characteristics of the lesion area.

A large number of scholars use DWI or DTI technology to study the volume change of the lesion area in patients with cerebral ischemia as the condition changes; and use DTI technology to quantitatively analyze the diffusion isotropy and anisotropy of water molecules in the lesion area. In previous studies, manual methods were used to segment cerebral ischemic lesions, but manual segmentation is very time-consuming, and the segmentation results depend on the subjective judgment of the operator. Due to the influence of factors such as noise, local volume effect, intensity inhomogeneity and diffusion anisotropy, automatic or semi-automatic segmentation of cerebral ischemic regions in DWI and DTI images is still a difficult problem. The local volume effect is caused by the limited spatial resolution of the MRI scanning coil; the intensity inhomogeneity is caused by the radio frequency inhomogeneities; the intensity overlap is caused by the DWI or DTI image This is caused by the similarity between the ischemic lesion area of the midbrain and the strength of the cranial nerve fibers.

The literature on automatic or semi-automatic segmentation of cerebral ischemic lesions in DWI and DTI images is very limited. Martel et al. proposed a semi-automatic segmentation method, that is, adaptive threshold segmentation that absorbs space constraints; and iterative conditional mode (ICM) method is used to find the local optimal solution. However, they could not satisfactorily distinguish the lesion from the nerve bundle due to the influence of intensity overlap caused by diffusion anisotropy.

For the segmentation of lesion regions in conventional MR images, an atlas-based segmentation method is usually used. Using nonlinear registration methods, anatomical templates can successfully identify different normal anatomical structures. However, the lesion area cannot be generated using a normal anatomical template, so it is impossible to obtain the lesion area by direct segmentation using the atlas. Leemput et al. used a statistical classification method to automatically segment different tissue structures in nuclear magnetic (MR) images, using the atlas of normal people as the initial segmentation and geometric shape constraints of normal tissue, and set the brain lesion area as outliers. This method was successfully applied to the segmentation of multiple sclerosis lesions in MR images. Based on Leemput's method, Moon et al. changed the spatial map, took the lesion tissue as prior knowledge, and roughly set the location of the lesion. However, due to the low contrast and anisotropy of diffusion images, none of these methods are suitable for the segmentation of brain infarct regions in DTI images.

Some methods to solve the local volume effect have been proposed one after another. Laidlaw et al. used the gray histogram based on the voxel region to represent the mixture of different tissues of the voxel, and used the Bayesian probability approach to match the gray histogram to determine the most likely mixture of different tissues within a single voxel. However, it is not clear how many tissue classes the intensity of a voxel is mixed from, and the algorithm ignores the influence of intensity inhomogeneity. Shattuck et al. and Noe et al. (2006) introduced local volumetric voxels as a new tissue class and then estimated the possible mixture of pure tissues in each voxel. However, this approach may cause over-smoothing of the classification results.

Rajapakse et al utilized a statistical model to represent the distribution of the main tissue classes, and the intensity measurement model fully considered the effects of noise and intensity inhomogeneity. Segmentation results on many clinical routine brain MR images demonstrate the robustness and sufficient accuracy of the proposed algorithm. However, the algorithm still has its limitations: the local volume effect is not considered; the segmentation result depends on the initial segmentation; the algorithm is not suitable for the segmentation of the lesion, even for conventional brain MR images.

Based on the characteristics of DTI images and existing image processing methods, we propose a new adaptive method to automatically segment cerebral ischemic lesions in DTI images of stroke patients. The method takes full account of noise, diffusion anisotropy, local volume effect and intensity inhomogeneity.

Contents of the invention

The purpose of the present invention is to provide an automatic method for segmenting cerebral ischemic lesions in DTI images, which fully considers the influence of noise, diffusion anisotropy, local volume effect and intensity inhomogeneity, and proposes a method based on multi-scale statistics The automatic segmentation method of classification and local volume classification assists clinicians in qualitative and quantitative diagnosis and guides treatment.

The core idea of the present invention is that we propose a brand-new self-adaptive method to automatically segment the cerebral ischemic lesion area in the DTI image of a stroke patient. The method includes the following steps: image preprocessing, calculation of diffusion tensor field, measurement of diffusion anisotropy, adaptive multi-scale statistical classification (MSSC for short), and local volume voxel reclassification ( partial volume voxel reclassification, referred to as PVVR). The adaptive MSSC model takes into account the spatial information of DTI images, intensity gradient, diffusion anisotropy, and tissue characteristics; the PVVR model uses local parameter information to improve the accuracy of local volume segmentation.

Based on the above purpose and ideas, the algorithms for automatically segmenting cerebral ischemic lesions in DTI images based on multi-scale statistical classification and local volume classification methods include:

(1) Image preprocessing, filtering the original image;

(2) Diffusion tensor field (tensor field) calculation, to obtain the tensor field corresponding to each voxel in the three-dimensional space;

(3) Measurement of diffusion anisotropy, which quantifies the anisotropy of each voxel in three-dimensional space;

(4) Calculation of the scale space, including the scale space of the original DTI image and the scale space of the diffusion anisotropy map;

(5) Adaptive multi-scale statistical classification (MSSC for short), while looking for the optimal lesion area, it overcomes the influence caused by noise, diffusion anisotropy and intensity inhomogeneity;

(6) Partial volume voxel reclassification (PVVR for short), on the basis of adaptive multi-scale statistical classification, further optimizes the segmentation results and overcomes the interference caused by the local volume effect.

The present invention uses self-adaptive multi-scale statistical classification and local volume voxel reclassification to effectively overcome the influence of noise, diffusion anisotropy, local volume effect and intensity inhomogeneity, and realizes automatic detection of cerebral ischemic lesion areas in DTI images. segmentation. It has important application value in the fields of medical image aided diagnosis system, medical image three-dimensional reconstruction system, and clinical pathology qualitative and quantitative diagnosis analysis.

Description of drawings

Figure 1. A block diagram of a method for automatically segmenting cerebral ischemic lesions in DTI images based on multi-scale statistical classification and local volume classification methods;

Fig. 2. A slice of the diffusion tensor volume data of a patient with acute cerebral apoplexy; each sub-image in the figure represents a scalar map of a component of the diffusion tensor D at that slice;

Figure 3. Diffusion anisotropy measurement of the tensor section in Figure 1; where: (a) trace map; (b) FA map;

Figure 4. Diagram of scale space;

Figure 5. Possible boundary conditions between different tissue classes after MSSC classification, where: (a) shows a region composed of two tissue classes; (b) shows a boundary composed of three tissue classes;

Figure 6. Comparison of segmentation results of different segmentation methods for DTI images, in which: (a) original DTI image of cerebral ischemia patients; (b) adaptive MAP segmentation under better initial segmentation conditions, where the arrow Pointing to the cranial nerve bundle that was misclassified as the lesion; (c) MSSC segmentation; (d) MSSC-PVVR segmentation;

Figure 7. Comparison of segmentation results of different segmentation methods for DTI images, in which: (a) original DTI image of cerebral ischemia patients; (b) adaptive MAP segmentation under better initial segmentation conditions, where the arrow Pointing to the cranial nerve bundle that was misclassified as the lesion; (c) MSSC segmentation; (d) MSSC-PVVR segmentation;

Figure 8. Comparison of segmentation results of different segmentation methods for DTI images, (a) original DTI image of cerebral ischemia patient; (b) adaptive MAP segmentation under the condition of better initial segmentation, where the arrow points to the wrong Cranial nerve bundles divided into lesion areas; (c) MSSC segmentation; (d) MSSC-PVVR segmentation.

Detailed ways

The automatic segmentation method of the present invention will be described in detail below in conjunction with the accompanying drawings. As a specific implementation scheme, the structural block diagram is shown in Figure 1. The segmentation method includes the following steps: image preprocessing, calculation of diffusion tensor field, measurement of diffusion anisotropy, adaptive multi-scale statistical classification, and local volume Voxel reclassification.

It mainly includes four steps: (1) estimation of diffusion tensor and diffusion anisotropy of DTI images; (2) calculation of scale space; (3) multi-scale statistical classification; (4) local volume voxel reclassification. The following introduces them one by one.

Step 1: Estimate the diffusion tensor and diffusion anisotropy of the DTI image

DTI is used to measure the diffusion characteristics of water molecules in biological tissues. Diffusion is a three-dimensional process. However, due to the structural characteristics of biological tissues, the movement of water molecules is not equal in all three-dimensional directions. The diffusion tensor is usually used to fully describe the motion characteristics of water molecules along different coordinate axes, as well as the interrelationship between them.

$\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; =</span>\left[\begin{array}{ccc}{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xy</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xz</span>}}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; yx</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; yy</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}\\ {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; zx</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; zy</span>}}& {\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; zz</span>}}\end{array}\right]$

D stands for Diffusion Tensor. Calculating the tensor D from the original DTI image is more complicated, and the detailed method Bihan has described in detail in the reference. Figure 2 represents a slice of the diffusion tensor volume data for an acute stroke patient. Each sub-image in Fig. 2 represents a scalar map of a component of the diffusion tensor D at that level.

Using the eigenvalues λ ₁ , λ ₂ , λ ₃ of the tensor D, where λ ₁ >λ ₂ >λ ₃ , different anisotropy measures can be obtained. In this paper, we use fractional anisotropy (FA for short) to quantitatively estimate the diffusion anisotropy.

$\mathrm{<span\; class="notranslate">\; FA</span>}<span\; class="notranslate">\; =</span>\sqrt{\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Tr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Tr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; Tr</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; D.</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}<span\; class="notranslate">\; /</span>\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

Tr(D)=(λ ₁ +λ ₂ +λ ₃ )/3

where Tr(D) is the trace of D, representing the average diffusivity in different directions. Figure 3 shows the trace ( trace) diagram and distribution anisotropy (FA) diagram of the tensor section in Figure 2. From Figure 3(b), it can be observed that the anisotropy of normal white matter regions is significantly higher than that of gray matter and CSF regions.

Step 2: Calculate the scale space

Scale spaces can be generated based on many different criteria. Linear scale space techniques tend to blur important features of images, such as the boundaries of different tissue structures. The non-linear scale space overcomes this shortcoming, making smoothing within a region greater than smoothing between regions. Perona and Malik proposed a partial differential equation for computing nonlinear scale spaces. The central idea is to introduce edge detection while filtering, allowing interaction between different scale levels.

$\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; t</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; div</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&Delta;y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>$

c(i,t)=g(|y(i,t)|)

In our segmentation method, y(i, t) represents the image intensity value of the DTI image at scale level t, position i; c(i, t) is the diffusion parameter, which varies depending on the spatial position, and is the variation of the image intensity The function of the modulus; div represents the divergence operator;  and Δ represent the gradient operator and the Laplacian operator, respectively. In this paper, we adopt the following diffusion function g( ) to generate the scale space.

$\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; Ks</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

The constant Ks is either set manually or generated using the method proposed by Canny.

Figure 4 shows a schematic diagram of the scale space. Different scale levels t represent different image spatial resolutions. Scale level t=0 represents the original image, the highest resolution in the scale space. As the scale level increases, the image becomes more blurred and contains less and less image information. High-resolution images have a close correspondence with low-resolution images, which facilitates us to extract overall structural information from low-resolution images and obtain detailed information from high-resolution images.

Step 3: Multiscale Statistical Classification (MSSC)

An image is composed of a collection of voxels that are adjacent to each other. I represents the coordinate position of the voxel in the image, y=(y _i , i∈I) represents the intensity value of the image, and y _i represents the intensity value of the image at the voxel position i. Set the number of tissue classes of the image as K, and each tissue class is represented by a numerical value in a set Λ={1, 2...k}; the segmentation of the image is actually to classify each voxel into different tissue classes. _xi = k means that the voxel at position i belongs to tissue class k, k∈Λ. x=( _xi , i∈I) represents a classification result of image y.

The process of segmentation is to find the appropriate x to represent the correct tissue class that the image y belongs to at each voxel position. We segment the original image using maximum a posteriori (MAP) estimation. Let x=x ^* represent the optimal split

${\mathrm{<span\; class="notranslate">\; x</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Omega;</span>}}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>$

where Ω represents all possible segmentations, and p(x|y) represents the probability of obtaining x segmentation given image y. Since the prior probability p(y) is independent of the split x, according to Bayesian theory,

p(x|y)∝p(x, y)=p(y|x)p(x)

Assuming that the noise of the image conforms to the Gaussian white noise distribution, if _xi =k, then

${\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ~</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

where μ _{k , i} , n _{k , I} and σ _{k , i} denote the mean intensity of tissue class k at position i, the noise, and the standard deviation of the noise, respectively. θ={θ _i , i∈I} represents the parameter set of the measurement model, θ _i ={θ _{k, i} =(μ _{k,, i} , σ _{k,, i} ), k∈Λ}. Represents the mean and standard deviation of each voxel of the tissue class in the image, taking into account the variation of biological tissue and the inhomogeneity of the spatial intensity of the image.

Assuming that R _k represents all voxel positions belonging to tissue class k, then the conditional probability p(y|x) can be written as

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\sqrt{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \}</span>$

We use Markov Random Field (MRF for short) to define the prior model, then the probability p(x) obeys the Gibbs distribution,

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\underset{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>$

Where β is a normalization constant, C represents a set of voxel points, and the voxels in the set are adjacent to each other.

we got

p(x|y)∝exp{-U(x)}

U(x) is an energy function, as follows

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; log</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}\underset{\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>$

The first two terms of U(x) represent the mutual constraint relationship between the original image data and the segmentation result; the last term represents the smooth constraint of the prior model on the segmentation result. The maximum a posteriori (MAP) estimation problem for finding partitions is equivalent to the minimization problem of the energy function U(x).

In step 2, we obtain sequential images at different resolutions. As we increase the scale level, the detail information of the image decreases. The blurred image sequence is denoted by y(t)=(y(i, t), i∈I, t∈N), N={1, 2...n}. (t represents the scale level, n represents the highest scale level). The corresponding segmentation for y(t) is denoted by x(t), x(t)=(x(i, t), i∈I).

If the segmentation x(t+1) is obtained at scale level t+1, then the parameter θ(t+1) can be estimated accordingly. Applying the known parameter θ(t+1), we can obtain a new segmentation of the image y(t) at scale level t. The corresponding parameter θ(t+1) of the segmentation result x(t+1) at scale level t+1 can be used to obtain the next segmentation at scale level t. After completing N iterations of segmentation and parameter estimation, when the original image with the highest resolution (t=0) is reached, we obtain the final optimal segmentation result. Therefore, segmentation can be described by the following two processes:

$\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; min</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; max</span>}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>$

The model parameters of each tissue class are known to estimate the most likely segmentation; the segmentation is known to estimate the optimal model parameters. The selection of measurement model parameters is based on the principle of maximization of image data. The adaptive multi-scale statistical classification (MSSC) process goes through multiple iterations to estimate the minimum value of the energy function U(t). U _i (t) represents the local energy function at position i at scale level t, as follows:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; log</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>$

where μ _{k,, i} (t) and σ _{k,, i} (t) are respectively μ _{k,, i} and σ _{k,, i} of the DTI image at scale level t. Here V _c ( _xi (t)) is defined as the number of voxels satisfying x _j (t)= _xi (t), i, j∈C.

In DTI images, the cerebral ischemic lesion area shows high signal, and due to the influence of anisotropy, the white matter nerve fibers also show high signal. Due to the overlap of intensity values, it is very difficult to accurately segment the cerebral ischemic lesion. We address this issue by including a control for diffusion anisotropy in the model.

α _i (t)=|y _i (t)-r _i (t)|

r _i (t)=α·FA _i (t) r _i (t) represents the distribution anisotropy value FA _i (t) of the original DTI image at position i at scale level t. The factor a ensures that FA has a consistent intensity space with y. α _i (t) describes the difference between y _i (t) and r _i (t). We modify the energy function U _i (t) formula as follows:

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arg</span>}\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; min</span>}}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; log</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&beta;V</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; \}</span>$

where γ is a normalization constant.

We can obtain the measurement model parameters θ(t)={ _θi (t), i∈I} at scale level t, where _θi (t)={θk _,i (t)=(μk _,,i (t), σ _{k,, i} (t)), k ∈ Λ}. By partial differentiation of log p(y(t)|x(t), θ(t+1)) with respect to μ _{k,, i} (t) and σ _{k,, i} (t), and make it zero . Estimates of μ _{k,, i} (t) and σ _{k,, i} (t) can be obtained as follows:

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>}$

where R _k (t) represents all regions belonging to tissue class k at scale level t, ie the set of voxel locations.

Step 4: Partial Volumetric Voxel Reclassification (PVVR)

Due to the local volume effect caused by the low spatial resolution of the image, voxels at the edge of the segmented region may be misclassified. Shattuck and Noe classified local volume voxels as a new tissue class to deal with local volume effects when segmenting conventional MR images. But this method is not suitable for the segmentation of DTI images. DTI images have very low contrast, and it is even difficult to distinguish white matter from gray matter; and local volumetric voxels often have similar intensity values to pure tissue classes. All these make the segmentation of DTI images more difficult than conventional MR images. To address this issue, after classification with adaptive Multi-Scale Statistical Classification (MSSC), we detect edge regions of different classes and reclassify local volumetric voxels to further refine the segmentation results. We use the Canny edge detector to detect the edge regions of different tissue classes. We segment the results using a multi-scale statistical classification (MSSC) method to estimate possible tissue margins in the original DTI image. Since the internal gray values of different tissue classes are equal in the segmentation results, edge detection between tissue classes is easy to estimate. Voxels in the edge region are considered as possible local volume voxels, and these voxels are reclassified using the local volume voxel reclassification (PVVR) method. Figure 5 illustrates possible boundary cases between different tissue classes after multiscale statistical classification (MSSC) classification. Misclassification of local volume voxels may occur in both cases of Fig. 5(a) and (b).

We consider the local volume voxel to be a linear union of different tissue classes that have been segmented,

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; p</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; )</span>$

θ={θ _i , i∈I}, where θ _i =(μ _{k,, i} , σ _{k,, i} ), k∈Λ}, represents known measurement model parameters. θ = θ(0) is obtained directly from the segmentation results of Multi-Scale Statistical Classification (MSSC). π _i,k represents the weight value at the position of possible local volume voxel i, 0<π _i,k <=1.

The weights of different classes on the local volume voxels are determined by solving the above formula. According to reality, we think that the local volume voxel is composed of two different classes k ₁ and k ₂ .

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}$

θ ¹ _i =(μ ^1, _{k, i} , σ ¹ _{k, i} ), k∈Λ, represents the average intensity and standard deviation of tissue class k in region R ¹ _i adjacent to position i.

${\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; |</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; |</span>}$

Where |R ¹ _{k, 1} | represents the total number of voxels belonging to tissue class k contained in the middle region R ¹ _i . In order to overcome the inhomogeneity of the intensity of the original DTI image, θ _i is replaced by θ ¹ _i .

$\mathrm{<span\; class="notranslate">\; o</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}^{\mathrm{<span\; class="notranslate">\; l</span>}}}_{{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}_{{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}$

Since the image intensity distribution y is known, and the measurement model parameters θ can be obtained by multi-scale statistical classification (MSSC), the classification x, θ ¹ _i = (μ ^1, _{k, i} , σ ¹ _{k, i} ), k∈Λ, It can be obtained conveniently; by solving π _{i, k} , and then reclassifying the local volume voxels into tissue classes with larger weights.

operation result

To further verify our algorithm, we selected 20 DTI images of cerebral ischemia patients. These DTI images were acquired by GE 1.5T or 3.0T nuclear magnetic system, using diffusion tensor imaging (TR/TE: 6000-7000/98ms; acquisition matrix: 128×128; scanning axis; FOV: 24cm; slice thickness 5mm; spacing 1.0mm; b value: 1000s/mm ² ; diffusion direction: 13 directions). In the stage of acute or subacute cerebral apoplexy, the cerebral ischemic lesion area presents high signal in DTI images. We classified images into three distinct tissue classes K=3: CSF, white and gray matter, and ischemic lesion.

Adaptive multi-scale statistical classification (MSSC)-volume voxel reclassification (PVVR) method effectively improves the segmentation accuracy of cerebral ischemic lesions in DTI images. We compared several segmentation methods: adaptive maximum a posteriori (MAP) segmentation, adaptive multiscale statistical classification (MSSC) segmentation, adaptive multiscale statistical classification (MSSC)-partial volumetric voxel reclassification (PVVR )segmentation. As shown in Figure 6, Figure 7, and Figure 8. (Figure 2, Figure 3 and Figure 6 are all from the same set of DTI data) Here, the initialization of adaptive maximum a posteriori estimation (MAP) segmentation adopts better threshold segmentation results; Experimental Estimation (MAP) segmentation will perform far worse than current performance. However, adaptive multi-scale statistical classification (MSSC) segmentation and adaptive multi-scale statistical classification (MSSC)-partial volumetric voxel reclassification (PVVR) segmentation methods use region splitting and merging algorithms to complete the initial segmentation. Experimental estimation (MAP) segmentation is more robust and convenient. It can be clearly seen from the experimental results that adaptive maximum a posteriori estimation (MAP) segmentation cannot effectively solve the problem of overlapping intensity values; adaptive multi-scale statistical classification (MSSC) segmentation and adaptive multi-scale statistical classification (MSSC)-local The Volumetric Voxel Reclassification (PVVR) segmentation method solves this problem well because it absorbs the control of diffusion anisotropy in the model; it is compatible with adaptive maximum a posteriori estimation (MAP) segmentation and adaptive multi-scale statistical classification ( Compared with the MSSC) segmentation method, the adaptive multi-scale statistical classification (MSSC)-local volume voxel reclassification (PVVR) segmentation effectively reduces the influence of the local volume effect.

Claims (5)

1. the automatic division method of a cerebral ischemia focal zone is cut apart DTI image cerebral ischemia focal zone automatically based on multiple dimensioned statistical classification and local volume sorting technique, it is characterized in that, may further comprise the steps:

(1) image pre-service is carried out filtering to original image;

(2) calculate the dispersion tensor field, obtains the pairing tensor field of each voxel of three dimensions;

(3) the anisotropic measurement of disperse quantizes the anisotropy of each voxel of three dimensions;

(4) calculating of metric space comprises original DTI graphical rule space, and disperse anisotropy mapping graph metric space;

(5) self-adapting multi-dimension statistical classification in the focus zone of seeking based on optimum, overcomes the influence that is brought owing to noise, disperse anisotropic and intensity non-uniformity;

(6) local volume voxel is classified again, on the basis of self-adapting multi-dimension statistical classification, further optimizes segmentation result, overcomes the interference that local volume effect brings.

2. the method for claim 1 is characterized in that, in (3) step, adopts the distribution anisotropy, quantitatively estimates the disperse anisotropy, and its formula is as follows:

$\mathrm{FA}=\sqrt{3\&lsqb;{({\mathrm{\&lambda;}}_1-\mathrm{Tr}\left(D\right))}^2+{({\mathrm{\&lambda;}}_2-\mathrm{Tr}\left(D\right))}^2+{({\mathrm{\&lambda;}}_3-\mathrm{Tr}\left(D\right))}^2\&rsqb;}/\sqrt{2({\mathrm{\&lambda;}}_1^2+{\mathrm{\&lambda;}}_2^2+{\mathrm{\&lambda;}}_3^2)}$

Tr(D)＝(λ ₁+λ ₂+λ ₃)/3

Wherein Tr (D) is the mark of D, represents the average dispersity of each different directions.

3. the method for claim 1 is characterized in that, in (4) step, the spread function g () below adopting produces metric space:

$g\left(\right|\&dtri;y(i,t)\left|\right)=e^{(-{\left(\right|\&dtri;y{(i,t)}_l|/\mathrm{Ks})}^2)}$

Constant Ks produces with the manual method of setting or using Canny to propose.

4. the method for claim 1, it is characterized in that, in (6) step, utilize after the self-adapting multi-dimension statistical classification,, detect the fringe region of different tissues class with edge detector, use the segmentation result of multiple dimensioned statistical classification method again, estimate the organization edge of possible original DTI image, the voxel of fringe region is possible local volume voxel, to these voxels with local volume voxel again sorting technique carry out subseries again.

5. method as claimed in claim 4 is characterized in that, described edge detector is the Canny edge detector.

Images