Anisotropic Diffusion

The ability of Minkowski Functionals to characterize local structure in different biological tissue types has been demonstrated in a variety of medical image processing tasks. We introduce anisotropic Minkowski Functionals (AMFs) as a novel variant that captures the inherent anisotropy of the underlying gray-level structures. To quantify the anisotropy characterized by our approach, we further introduce a method to compute a quantitative measure motivated by a technique utilized in MR diffusion tensor imaging, namely fractional anisotropy. We showcase the applicability of our method in the research context of characterizing the local structure properties of trabecular bone micro-architecture in the proximal femur as visualized on multi-detector CT. To this end, AMFs were computed locally for each pixel of ROIs extracted from the head, neck and trochanter regions. Fractional anisotropy was then used to quantify the local anisotropy of the trabecular structures found in these ROIs and to compare its distribution in different anatomical regions. Our results suggest a significantly greater concentration of anisotropic trabecular structures in the head and neck regions when compared to the trochanter region (p < 10-4). We also evaluated the ability of such AMFs to predict bone strength in the femoral head of proximal femur specimens obtained from 50 donors. Our results suggest that such AMFs, when used in conjunction with multi-regression models, can outperform more conventional features such as BMD in predicting failure load. We conclude that such anisotropic Minkowski Functionals can capture valuable information regarding directional attributes of local structure, which may be useful in a wide scope of biomedical imaging applications.

Corner detection is a method used in computer vision systems to extract certain features and deduce the contents. Corner detection is used frequently in video tracking, stitching motion
detection and object recognition. Corner detection overlaps with the topic of interest point detection.
Here the objective is to use Harris corner detection to stitch two different images together. It picks corners because, since it is the intersection of two edges, it represents a point in
which the directions of these two edges change. Hence, the gradient of the image (in both directions) have a high variation, which can be used to detect it.

The taphonomic study of Petit-Bost, Croix-de-Canard and Cantalouette II, three Palaeolithic sites that were recently discovered near Périgueux and Bergerac (Dordogne, France) in a colluvial context, has enlightened the difficulty of adequately appreciating the relative role of cultural and natural processes in site spatial patterning. Periglacial solifluction was thought to have played a significant role in site formation. Because the nature of the modifications induced by solifluction was still poorly understood, a simulation was made using data of soil movement recorded at La Mortice (French Southern Alps, 3100 m in elevation) in a modern periglacial environment. The results show that, for a knapping location, the first steps of deformation are typified both by a downslope translation of the location center and by an anisotropic diffusion of the artifacts. The knapping spot becomes elongated along the slope, with a dense relic concentration of artifacts in the upslope portion. This type of pattern has been obtained after 100–200 years of simulated displacement according to the climatic and soil conditions that characterise the La Mortice site. The ultimate stages of deformation show that the artifact distribution tends to homogenise on larger surfaces and resemble a random distribution. The ability of the simulated patterns to closely fit those observed in archaeological contexts is evaluated at three sites from Southwestern France. At Petit-Bost, the hypothesis of limited solifluction explains accurately the association of both cultural (artifact concentrations) and natural (artifact preferred orientation) features. At Croix-de-Canard, long-term solifluction can be proposed. By contrast, the simulated patterns do not describe the structures observed on the steeper slopes at Cantalouette II, where the knapping spot transforms into distinct solifluction lobes.

In this paper we present an anisotropic filter for speckle reduction in ultrasound images and an adaptation of the geodesic active contours technique for the segmentation of breast tumors. The anisotropic diffusion we propose is based on a texture description provided by a set of Gabor filters and allows reducing speckle noise while preserving edges. Furthermore, it is used to extract an initial pre-segmentation of breast tumors which is used as initialization for the active contours technique. This technique has been adapted to the characteristics of ultrasonography by adding certain texture-related terms which provide a better discrimination of the regions inside and outside the nodules. These terms allow obtaining a more accurate contour when the gradients are not high and uniform.

Image abstraction is an increasingly important task in various multimedia applications. It involves the artificial transformation of photorealistic images into cartoon-like images. To simplify image content, the bilateral and Kuwahara filters remain popular choices to date. However, these methods often produce undesirable over-blurring effects and are highly susceptible to the presence of noise. In this paper, we propose an image abstraction technique that balances region smoothing and edge preservation. The coupling of a classic Symmetric Nearest Neighbor (SNN) filter with anisotropic diffusion within our abstraction framework enables effective suppression of local patch artifacts. Our qualitative and quantitative evaluation demonstrate the significant appeal and advantages of our technique in comparison to standard filters in literature.

In this paper we propose and compare two approaches, based on the level set method in order to extract the coastline from SAR (Synthetic Aperture Radar) images. A coast- line is the boundary between land and sea. Detecting the coastline is of fundamental importance when monitoring various natural phenomena such as tides, coastal erosion and the dynamics of glaciers. In this case SAR images show problems which arise from the presence of the speckle noise and of the strong signal deriving from the rough or slight sea. In fact in the case of heavy sea the signal determines an intensity similar to the one of land, making it difficult to distinguish the coastline. [ DOI : 10.1685/CSC09249] About DOI

This paper is concerned with partial differential equation (PDE)-based image denoising for random-valued impulse noise. We introduce the notion of ENI (the abbreviation for “edge pixels, noisy pixels, and interior pixels”) that denotes the number of homogeneous pixels in a local neighborhood and is significantly different for edge pixels, noisy pixels, and interior pixels. We redefine the controlling speed function and the controlling fidelity function to depend on ENI. According to our two controlling functions, the diffusion and fidelity process at edge pixels, noisy pixels, and interior pixels can be selectively carried out. Furthermore, a class of second-order improved and edge-preserving PDE denoising models is proposed based on the two new controlling functions in order to deal with random-valued impulse noise reliably. We demonstrate the performance of the proposed PDEs via application to five standard test images, corrupted by random-valued impulse noise with various noise levels and comparison with the related second-order PDE models and the other special filtering methods for random-valued impulse noise. Our two controlling functions are extended to automatically other PDE models.

A mathematical model for a nonlinear image multiscale analysis is studied. Processing of an image is based on a solution of the strongly nonlinear parabolic partial differential equation, which can degenerate depending on values of the greylevel intensity function. The governing PDE is a generalization of the regularized (in the sense of Catté, Lions, Morel and Coll) Perona-Malik anisotropic diffusion equation. We present numerical techniques for solving the suggested initial-boundary value problem and also existence and convergence results. Numerical experiments are discussed.

In this paper we show that a classic optical flow technique by Nagel and Enkelmann (1986, IEEE Trans. Pattern Anal. Mach. Intell., Vol. 8, pp. 565–593) can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that (i) avoid inconsistencies caused by centering the brightness term and the smoothness term in different images, (ii) use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and (iii) create an energy functional that is invariant under linear brightness changes. Applying a gradient descent method to the resulting energy functional leads to a system of diffusion–reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100 % density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the optical flow methods with 100 % density that are evaluated by Barron et al. (1994, Int. J. Comput. Vision, Vol. 12, pp. 43–47). Our software is available from the Internet.