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Keywords = computer vision color constancy

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12 pages, 2927 KiB  
Article
CVCC Model: Learning-Based Computer Vision Color Constancy with RiR-DSN Architecture
by Ho-Hyoung Choi
Sensors 2023, 23(11), 5341; https://doi.org/10.3390/s23115341 - 5 Jun 2023
Cited by 3 | Viewed by 1742
Abstract
To achieve computer vision color constancy (CVCC), it is vital but challenging to estimate scene illumination from a digital image, which distorts the true color of an object. Estimating illumination as accurately as possible is fundamental to improving the quality of the image [...] Read more.
To achieve computer vision color constancy (CVCC), it is vital but challenging to estimate scene illumination from a digital image, which distorts the true color of an object. Estimating illumination as accurately as possible is fundamental to improving the quality of the image processing pipeline. CVCC has a long history of research and has significantly advanced, but it has yet to overcome some limitations such as algorithm failure or accuracy decreasing under unusual circumstances. To cope with some of the bottlenecks, this article presents a novel CVCC approach that introduces a residual-in-residual dense selective kernel network (RiR-DSN). As its name implies, it has a residual network in a residual network (RiR) and the RiR houses a dense selective kernel network (DSN). A DSN is composed of selective kernel convolutional blocks (SKCBs). The SKCBs, or neurons herein, are interconnected in a feed-forward fashion. Every neuron receives input from all its preceding neurons and feeds the feature maps into all its subsequent neurons, which is how information flows in the proposed architecture. In addition, the architecture has incorporated a dynamic selection mechanism into each neuron to ensure that the neuron can modulate filter kernel sizes depending on varying intensities of stimuli. In a nutshell, the proposed RiR-DSN architecture features neurons called SKCBs and a residual block in a residual block, which brings several benefits such as alleviation of the vanishing gradients, enhancement of feature propagation, promotion of the reuse of features, modulation of receptive filter sizes depending on varying intensities of stimuli, and a dramatic drop in the number of parameters. Experimental results highlight that the RiR-DSN architecture performs well above its state-of-the-art counterparts, as well as proving to be camera- and illuminant-invariant. Full article
(This article belongs to the Collection Computational Imaging and Sensing)
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<p>Typical (<b>a</b>) basic architecture and its (<b>b</b>) basic block.</p>
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<p>Typical (<b>a</b>) basic architecture and its (<b>b</b>) basic block.</p>
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<p>The proposed RiR-DSN architecture.</p>
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<p>Comparison of basic training rates.</p>
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<p>Accuracy comparison by (<b>a</b>) average angular error and (<b>b</b>) median angular error between the basic CNN and the proposed method.</p>
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<p>The resulting images from the proposed RiR-SDN architecture: (<b>a</b>) original image, (<b>b</b>) estimated illuminant, (<b>c</b>) ground truth image, and (<b>d</b>) corrected image with the Gehler and Shi dataset.</p>
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21 pages, 7862 KiB  
Article
Illuminant Estimation Using Adaptive Neuro-Fuzzy Inference System
by Yunhui Luo, Xingguang Wang, Qing Wang and Yehong Chen
Appl. Sci. 2021, 11(21), 9936; https://doi.org/10.3390/app11219936 - 25 Oct 2021
Cited by 1 | Viewed by 2416
Abstract
Computational color constancy (CCC) is a fundamental prerequisite for many computer vision tasks. The key of CCC is to estimate illuminant color so that the image of a scene under varying illumination can be normalized to an image under the canonical illumination. As [...] Read more.
Computational color constancy (CCC) is a fundamental prerequisite for many computer vision tasks. The key of CCC is to estimate illuminant color so that the image of a scene under varying illumination can be normalized to an image under the canonical illumination. As a type of solution, combination algorithms generally try to reach better illuminant estimation by weighting other unitary algorithms for a given image. However, due to the diversity of image features, applying the same weighting combination strategy to different images might result in unsound illuminant estimation. To address this problem, this study provides an effective option. A two-step strategy is first employed to cluster the training images, then for each cluster, ANFIS (adaptive neuro-network fuzzy inference system) models are effectively trained to map image features to illuminant color. While giving a test image, the fuzzy weights measuring what degrees the image belonging to each cluster are calculated, thus a reliable illuminant estimation will be obtained by weighting all ANFIS predictions. The proposed method allows illuminant estimation to be dynamic combinations of initial illumination estimates from some unitary algorithms, relying on the powerful learning and reasoning capabilities of ANFIS. Extensive experiments on typical benchmark datasets demonstrate the effectiveness of the proposed approach. In addition, although there is an initial observation that some learning-based methods outperform even the most carefully designed and tested combinations of statistical and fuzzy inference systems, the proposed method is good practice for illuminant estimation considering fuzzy inference eases to implement in imaging signal processors with if-then rules and low computation efforts. Full article
(This article belongs to the Topic Applied Computer Vision and Pattern Recognition)
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<p>Overview of the training phase and the testing phase for the proposed approach.</p>
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<p>Examples of membership functions used by the ANFIS models developed for (<b>a</b>) estimation of <span class="html-italic">r</span> component, (<b>b</b>) estimation of <span class="html-italic">g</span> component, and (<b>c</b>) estimation of <span class="html-italic">b</span> component. In these three models, the inputs are chromaticity values of <math display="inline"><semantics> <msub> <mi>r</mi> <mi>i</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>g</mi> <mi>i</mi> </msub> </semantics></math> (<math display="inline"><semantics> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> </mrow> </semantics></math>) from the unitary algorithms: GW, WP, PCA-based, and LSR, respectively. The curves in cyan, purple, yellow, and magenta indicate the membership values for the four cluster regions respectively, responding to the number of clusters to be 4.</p>
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<p>Example results for indoor scene from the Gehler-Shi dataset: (<b>a</b>) input image; (<b>b</b>) ground truth; (<b>c</b>) ours; (<b>d</b>) GW; (<b>e</b>) GGW; (<b>f</b>) WP; (<b>g</b>) GE1; (<b>h</b>) GE2; (<b>i</b>) SOG; (<b>j</b>) PCA-based; and (<b>k</b>) LSR, respectively. All images shown are rendered in sRGB color space.</p>
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<p>Example results for natural lighting scene taken from the Gehler-Shi dataset: (<b>a</b>) input image; (<b>b</b>) ground truth; (<b>c</b>) ours; (<b>d</b>) GW; (<b>e</b>) GGW; (<b>f</b>) WP; (<b>g</b>) GE1; (<b>h</b>) GE2; (<b>i</b>) SOG; (<b>j</b>) PCA-based; and (<b>k</b>) LSR, respectively. All images shown are rendered in sRGB color space.</p>
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<p>Example results for indoor scene taken from the Cube+ dataset: (<b>a</b>) input image; (<b>b</b>) ground truth; (<b>c</b>) ours; (<b>d</b>) GW; (<b>e</b>) GGW; (<b>f</b>) WP; (<b>g</b>) GE1; (<b>h</b>) GE2; (<b>i</b>) SOG; (<b>j</b>) PCA-based; and (<b>k</b>) LSR, respectively. All images shown are rendered in sRGB color space.</p>
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<p>Example results for outdoor natural lighting scene taken from the Cube+ dataset: (<b>a</b>) input image; (<b>b</b>) ground truth; (<b>c</b>) ours; (<b>d</b>) GW; (<b>e</b>) GGW; (<b>f</b>) WP; (<b>g</b>) GE1; (<b>h</b>) GE2; (<b>i</b>) SOG; (<b>j</b>) PCA-based; and (<b>k</b>) LSR, respectively. All images shown are rendered in sRGB color space.</p>
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<p>Example results for outdoor artificial lighting scene taken from the Cube+ dataset: (<b>a</b>) input image; (<b>b</b>) ground truth; (<b>c</b>) ours; (<b>d</b>) GW; (<b>e</b>) GGW; (<b>f</b>) WP; (<b>g</b>) GE1; (<b>h</b>) GE2; (<b>i</b>) SOG; (<b>j</b>) PCA-based; and (<b>k</b>) LSR, respectively. All images shown are rendered in sRGB color space.</p>
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<p>Boxplot and plot of minimum AEs’ distribution: (<b>a</b>) the distribution of the minimum AE across the 8 methods, and (<b>b</b>) the minimum AE distribution for each method versus minimum AE obtainable with chosen combination of methods. The value near the box of each unitary algorithm indicates the number of the corresponding algorithm with minimum AE across the 8 methods. It can be seen from the left subfigure that for most images there is at least one unitary algorithm to estimate its illuminant color resulting in AE no more than 3. This right subfigure shows the minimum AEs of the proposed method with the chosen combination outperforms most of the eight unitary algorithms, where No. of images 1~100 are the first 100 images in the Gehler-Shi dataset, and No. of images 101~200 the first 100 images in the Cube+ dataset. Due to limited length, we just show the results for 200 images.</p>
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16 pages, 3738 KiB  
Article
CNN-Based Illumination Estimation with Semantic Information
by Ho-Hyoung Choi, Hyun-Soo Kang and Byoung-Ju Yun
Appl. Sci. 2020, 10(14), 4806; https://doi.org/10.3390/app10144806 - 13 Jul 2020
Cited by 16 | Viewed by 2836
Abstract
For more than a decade, both academia and industry have focused attention on the computer vision and in particular the computational color constancy (CVCC). The CVCC is used as a fundamental preprocessing task in a wide range of computer vision applications. While our [...] Read more.
For more than a decade, both academia and industry have focused attention on the computer vision and in particular the computational color constancy (CVCC). The CVCC is used as a fundamental preprocessing task in a wide range of computer vision applications. While our human visual system (HVS) has the innate ability to perceive constant surface colors of objects under varying illumination spectra, the computer vision is facing the color constancy challenge in nature. Accordingly, this article proposes novel convolutional neural network (CNN) architecture based on the residual neural network which consists of pre-activation, atrous or dilated convolution and batch normalization. The proposed network can automatically decide what to learn from input image data and how to pool without supervision. When receiving input image data, the proposed network crops each image into image patches prior to training. Once the network begins learning, local semantic information is automatically extracted from the image patches and fed to its novel pooling layer. As a result of the semantic pooling, a weighted map or a mask is generated. Simultaneously, the extracted information is estimated and combined to form global information during training. The use of the novel pooling layer enables the proposed network to distinguish between useful data and noisy data, and thus efficiently remove noisy data during learning and evaluating. The main contribution of the proposed network is taking CVCC to higher accuracy and efficiency by adopting the novel pooling method. The experimental results demonstrate that the proposed network outperforms its conventional counterparts in estimation accuracy. Full article
(This article belongs to the Section Applied Industrial Technologies)
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<p>Block diagram of the proposed method.</p>
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<p>Proposed deep convolutional neural network (DCNN) architecture with pre-activation, atrous convolution, and batch-normalization.</p>
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<p>Total training loss comparison in the logarithm space of four different learning rates to optimize the base learning rate.</p>
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<p>Comparison of median angular errors with and without semantic information (SI).</p>
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<p>Shi’s re-processed dataset and their resulting images: (<b>a</b>) original image, (<b>b</b>) illumination estimation map, (<b>c</b>) weighted map, (<b>d</b>) image <math display="inline"><semantics> <mo>×</mo> </semantics></math> weighted map, and (<b>e</b>) corrected image.</p>
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<p>Comparative angular error (AE) histogram of convolutional neural network (CNN)-based, exemplar-based, ensemble of decision (ED) tree based methods, DS-Net, AlexNet-FC, SqueezeNet-FC, CCATI, Zhan et al., and the proposed network (proposed net.) with Shi’s re-processed dataset and the NUS 8-Camera Dataset.</p>
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<p>Comparison of root mean square error (RMSE) results of CNN-based, exemplar-based, ensemble of decision (ED) tree based methods, DS-Net, AlexNet-FC4, SqueezeNet-FC4, CCATI, Zhan et al., and the proposed network (proposed) with the angular error as input.</p>
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<p>Comparison of the median angular errors of 321 different SFU-lab images.</p>
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<p>Comparison of the mean angular errors of 500 different gray-ball images.</p>
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15 pages, 4190 KiB  
Article
A Smart System for Low-Light Image Enhancement with Color Constancy and Detail Manipulation in Complex Light Environments
by Ziaur Rahman, Muhammad Aamir, Yi-Fei Pu, Farhan Ullah and Qiang Dai
Symmetry 2018, 10(12), 718; https://doi.org/10.3390/sym10120718 - 5 Dec 2018
Cited by 23 | Viewed by 4096
Abstract
Images are an important medium to represent meaningful information. It may be difficult for computer vision techniques and humans to extract valuable information from images with low illumination. Currently, the enhancement of low-quality images is a challenging task in the domain of image [...] Read more.
Images are an important medium to represent meaningful information. It may be difficult for computer vision techniques and humans to extract valuable information from images with low illumination. Currently, the enhancement of low-quality images is a challenging task in the domain of image processing and computer graphics. Although there are many algorithms for image enhancement, the existing techniques often produce defective results with respect to the portions of the image with intense or normal illumination, and such techniques also inevitably degrade certain visual artifacts of the image. The model use for image enhancement must perform the following tasks: preserving details, improving contrast, color correction, and noise suppression. In this paper, we have proposed a framework based on a camera response and weighted least squares strategies. First, the image exposure is adjusted using brightness transformation to obtain the correct model for the camera response, and an illumination estimation approach is used to extract a ratio map. Then, the proposed model adjusts every pixel according to the calculated exposure map and Retinex theory. Additionally, a dehazing algorithm is used to remove haze and improve the contrast of the image. The color constancy parameters set the true color for images of low to average quality. Finally, a details enhancement approach preserves the naturalness and extracts more details to enhance the visual quality of the image. The experimental evidence and a comparison with several, recent state-of-the-art algorithms demonstrated that our designed framework is effective and can efficiently enhance low-light images. Full article
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<p>Various conditions that negatively affect image quality, such as (<b>a</b>) bad weather; (<b>b</b>) dark light; (<b>c</b>) one side with darkness and one side with normal contrast; and (<b>d</b>) haze or fog.</p>
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<p>The general flowchart of the proposed framework. CRM = camera response model.</p>
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<p>Visual representation and comparison of the various methods. The odd rows show the results of various enhancement schemes, and the even rows show the extracted regions of interest (ROI).</p>
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<p>A comparison of the results of the handling of several visual artifacts. For example, in the first row, the sky color, clouds, wall texture, and dark regions were addressed. The haze and color were treated well in the images given in second row. The texture details, trees, and leaf colors were enhanced well in the images given in the third, fourth, and fifth rows, respectively.</p>
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<p>Lightness distortion visual representation and comparison of the various algorithms. The lightness error (LOE) value range is 0–5000. The lower values of the LOE indicate that the images were slightly degraded from light distortion, while the higher values of the LOE indicate that heavy light distortion occurred in the images.</p>
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<p>Results of the color distortion; the enhanced result can be zoomed in to clearly see the difference.</p>
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<p>Running time comparison of the various methods.</p>
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47 pages, 7691 KiB  
Article
AutoCloud+, a “Universal” Physical and Statistical Model-Based 2D Spatial Topology-Preserving Software for Cloud/Cloud–Shadow Detection in Multi-Sensor Single-Date Earth Observation Multi-Spectral Imagery—Part 1: Systematic ESA EO Level 2 Product Generation at the Ground Segment as Broad Context
by Andrea Baraldi and Dirk Tiede
ISPRS Int. J. Geo-Inf. 2018, 7(12), 457; https://doi.org/10.3390/ijgi7120457 - 26 Nov 2018
Cited by 13 | Viewed by 6334
Abstract
The European Space Agency (ESA) defines Earth observation (EO) Level 2 information product the stack of: (i) a single-date multi-spectral (MS) image, radiometrically corrected for atmospheric, adjacency and topographic effects, with (ii) its data-derived scene classification map (SCM), whose thematic map legend includes [...] Read more.
The European Space Agency (ESA) defines Earth observation (EO) Level 2 information product the stack of: (i) a single-date multi-spectral (MS) image, radiometrically corrected for atmospheric, adjacency and topographic effects, with (ii) its data-derived scene classification map (SCM), whose thematic map legend includes quality layers cloud and cloud–shadow. Never accomplished to date in an operating mode by any EO data provider at the ground segment, systematic ESA EO Level 2 product generation is an inherently ill-posed computer vision (CV) problem (chicken-and-egg dilemma) in the multi-disciplinary domain of cognitive science, encompassing CV as subset-of artificial general intelligence (AI). In such a broad context, the goal of our work is the research and technological development (RTD) of a “universal” AutoCloud+ software system in operating mode, capable of systematic cloud and cloud–shadow quality layers detection in multi-sensor, multi-temporal and multi-angular EO big data cubes characterized by the five Vs, namely, volume, variety, veracity, velocity and value. For the sake of readability, this paper is divided in two. Part 1 highlights why AutoCloud+ is important in a broad context of systematic ESA EO Level 2 product generation at the ground segment. The main conclusions of Part 1 are both conceptual and pragmatic in the definition of remote sensing best practices, which is the focus of efforts made by intergovernmental organizations such as the Group on Earth Observations (GEO) and the Committee on Earth Observation Satellites (CEOS). First, the ESA EO Level 2 product definition is recommended for consideration as state-of-the-art EO Analysis Ready Data (ARD) format. Second, systematic multi-sensor ESA EO Level 2 information product generation is regarded as: (a) necessary-but-not-sufficient pre-condition for the yet-unaccomplished dependent problems of semantic content-based image retrieval (SCBIR) and semantics-enabled information/knowledge discovery (SEIKD) in multi-source EO big data cubes, where SCBIR and SEIKD are part-of the GEO-CEOS visionary goal of a yet-unaccomplished Global EO System of Systems (GEOSS). (b) Horizontal policy, the goal of which is background developments, in a “seamless chain of innovation” needed for a new era of Space Economy 4.0. In the subsequent Part 2 (proposed as Supplementary Materials), the AutoCloud+ software system requirements specification, information/knowledge representation, system design, algorithm, implementation and preliminary experimental results are presented and discussed. Full article
(This article belongs to the Special Issue GEOBIA in a Changing World)
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<p>As in [<a href="#B16-ijgi-07-00457" class="html-bibr">16</a>], courtesy of the Food and Agriculture Organization (FAO of the United Nations (UN). Two-stage fully-nested FAO Land Cover Classification System (LCCS) taxonomy. The first-stage fully-nested 3-level 8-class FAO LCCS Dichotomous Phase (DP) taxonomy is general-purpose, user- and application-independent. It consists of a sorted set of three dichotomous layers: (i) vegetation versus non-vegetation, (ii) terrestrial versus aquatic, and (iii) managed versus natural or semi-natural. These three dichotomous layers deliver as output the following 8-class FAO LCCS-DP taxonomy. (A11) Cultivated and Managed Terrestrial (non-aquatic) Vegetated Areas. (A12) Natural and Semi-Natural Terrestrial Vegetation. (A23) Cultivated Aquatic or Regularly Flooded Vegetated Areas. (A24) Natural and Semi-Natural Aquatic or Regularly Flooded Vegetation. (B35) Artificial Surfaces and Associated Areas. (B36) Bare Areas. (B47) Artificial Waterbodies, Snow and Ice. (B48) Natural Waterbodies, Snow and Ice. The general-purpose user- and application-independent 3-level 8-class FAO LCCS-DP taxonomy is preliminary to a second-stage FAO LCCS Modular Hierarchical Phase (MHP) taxonomy, consisting of a battery of user- and application-specific one-class classifiers, equivalent to one-class grammars (syntactic classifiers) [<a href="#B19-ijgi-07-00457" class="html-bibr">19</a>].</p>
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<p>Multi-disciplinary cognitive science domain, adapted from [<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>,<a href="#B77-ijgi-07-00457" class="html-bibr">77</a>,<a href="#B78-ijgi-07-00457" class="html-bibr">78</a>,<a href="#B79-ijgi-07-00457" class="html-bibr">79</a>,<a href="#B80-ijgi-07-00457" class="html-bibr">80</a>,<a href="#B81-ijgi-07-00457" class="html-bibr">81</a>], where it is postulated that ‘Human vision → computer vision (CV)’, where symbol ‘→’ denotes relationship <span class="html-italic">part-of</span> pointing from the supplier to the client, not to be confused with relationship <span class="html-italic">subset-of</span>, ‘⊃’, meaning specialization with inheritance from the superset to the subset, in agreement with the standard Unified Modeling Language (UML) for graphical modeling of object-oriented software [<a href="#B86-ijgi-07-00457" class="html-bibr">86</a>]. The working hypothesis ‘Human vision → CV’ means that human vision is expected to work as lower bound of CV, i.e., a CV system is required to include as <span class="html-italic">part-of</span> a computational model of human vision [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B76-ijgi-07-00457" class="html-bibr">76</a>,<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B88-ijgi-07-00457" class="html-bibr">88</a>,<a href="#B89-ijgi-07-00457" class="html-bibr">89</a>,<a href="#B90-ijgi-07-00457" class="html-bibr">90</a>,<a href="#B91-ijgi-07-00457" class="html-bibr">91</a>,<a href="#B92-ijgi-07-00457" class="html-bibr">92</a>,<a href="#B93-ijgi-07-00457" class="html-bibr">93</a>,<a href="#B94-ijgi-07-00457" class="html-bibr">94</a>,<a href="#B95-ijgi-07-00457" class="html-bibr">95</a>,<a href="#B96-ijgi-07-00457" class="html-bibr">96</a>,<a href="#B97-ijgi-07-00457" class="html-bibr">97</a>,<a href="#B98-ijgi-07-00457" class="html-bibr">98</a>,<a href="#B99-ijgi-07-00457" class="html-bibr">99</a>,<a href="#B100-ijgi-07-00457" class="html-bibr">100</a>,<a href="#B101-ijgi-07-00457" class="html-bibr">101</a>,<a href="#B102-ijgi-07-00457" class="html-bibr">102</a>,<a href="#B103-ijgi-07-00457" class="html-bibr">103</a>,<a href="#B104-ijgi-07-00457" class="html-bibr">104</a>]. In practice, to become better conditioned for numerical solution, an inherently ill-posed CV system is required to comply with human visual perception phenomena in the multi-disciplinary domain of cognitive science. Cognitive science is the interdisciplinary scientific study of the mind and its processes. It examines what cognition (learning, adaptation, self-organization) is, what it does and how it works [<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>,<a href="#B77-ijgi-07-00457" class="html-bibr">77</a>,<a href="#B78-ijgi-07-00457" class="html-bibr">78</a>,<a href="#B79-ijgi-07-00457" class="html-bibr">79</a>,<a href="#B80-ijgi-07-00457" class="html-bibr">80</a>,<a href="#B81-ijgi-07-00457" class="html-bibr">81</a>]. It especially focuses on how information/knowledge is represented, acquired, processed and transferred either in the neuro-cerebral apparatus of living organisms or in machines, e.g., computers. Like engineering, remote sensing (RS) is a meta-science [<a href="#B105-ijgi-07-00457" class="html-bibr">105</a>], the goal of which is to transform knowledge of the world, provided by other scientific disciplines, into useful user- and context-dependent solutions in the world. Neuroscience, in particular neurophysiology, studies the neuro-cerebral apparatus of living organisms. Neural network (NN) is synonymous with distributed processing system, consisting of neurons as elementary processing elements and synapses as lateral connections. Is it possible and even convenient to mimic biological mental functions, e.g., human reasoning, by means of an artificial mind whose physical support is not an electronic brain implemented as an artificial NN (ANN)? The answer is no according to the “connectionists approach” promoted by traditional cybernetics, where a complex system always comprises an “artificial mind-electronic brain” combination. This is alternative to a traditional approach to artificial intelligence (AI), whose so-called symbolic approach investigates an artificial mind independently of its physical support [<a href="#B77-ijgi-07-00457" class="html-bibr">77</a>].</p>
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<p>Solar illumination geometries and viewpoint geometries in spaceborne and airborne EO image acquisition.</p>
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<p>In agreement with the standard Unified Modeling Language (UML) for graphical modeling of object-oriented software [<a href="#B86-ijgi-07-00457" class="html-bibr">86</a>], relationship <span class="html-italic">part-of</span>, denoted with symbol ‘→’ pointing from the supplier to the client, should not to be confused with relationship <span class="html-italic">subset-of</span>, ‘⊃’, meaning specialization with inheritance from the superset to the subset. A National Aeronautics and Space Administration (NASA) EO Level 2 product is defined as “a data-derived geophysical variable at the same resolution and location as Level 1 source data” [<a href="#B109-ijgi-07-00457" class="html-bibr">109</a>]. Herein, it is considered <span class="html-italic">part-of</span> an ESA EO Level 2 product defined as [<a href="#B11-ijgi-07-00457" class="html-bibr">11</a>,<a href="#B12-ijgi-07-00457" class="html-bibr">12</a>]: (a) a single-date multi-spectral (MS) image whose digital numbers (DNs) are radiometrically corrected into surface reflectance (SURF) values for atmospheric, adjacency and topographic effects, stacked with (b) its data-derived general-purpose, user- and application-independent scene classification map (SCM), whose thematic map legend includes quality layers cloud and cloud–shadow. In this paper, ESA EO Level 2 product is regarded as an information primitive to be accomplished by Artificial Intelligence for the Space segment (AI4Space), such as in future intelligent small satellite constellations, rather than at the ground segment in an AI for data and information access services (AI4DIAS) framework. In this graphical representation, additional acronyms of interest are computer vision (CV), whose special case is EO image understanding (EO-IU) in operating mode, semantic content-based image retrieval (SCBIR) [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B110-ijgi-07-00457" class="html-bibr">110</a>,<a href="#B111-ijgi-07-00457" class="html-bibr">111</a>,<a href="#B112-ijgi-07-00457" class="html-bibr">112</a>,<a href="#B113-ijgi-07-00457" class="html-bibr">113</a>,<a href="#B114-ijgi-07-00457" class="html-bibr">114</a>,<a href="#B115-ijgi-07-00457" class="html-bibr">115</a>], semantics-enabled information/knowledge discovery (SEIKD), where SCIR + SEIKD is considered synonym for AI4DIAS, and Global Earth Observation System of Systems (GEOSS), defined by the Group on Earth Observations [<a href="#B5-ijgi-07-00457" class="html-bibr">5</a>]. Our working hypothesis postulates that the following dependence relationship holds true. ‘NASA EO Level 2 product → ESA EO Level 2 product = AI4Space ⊂ EO-IU in operating mode ⊂ CV → [EO-SCBIR + SEIKD = AI4DIAS] → GEO-GEOSS’. This equation means that GEOSS, whose <span class="html-italic">part-of</span> are the still-unsolved (open) problems of SCBIR and SEIKD, cannot be achieved until the necessary-but-not-sufficient pre-condition of CV in operating mode, specifically, systematic ESA EO Level 2 product generation, is accomplished in advance. Encompassing both biological vision and CV, vision is synonym for scene-from-image reconstruction and understanding. Vision is a cognitive <span class="html-italic">(information-as-data-interpretation</span>) problem [<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>] very difficult to solve because: (i) non-deterministic polynomial (NP)-hard in computational complexity [<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B116-ijgi-07-00457" class="html-bibr">116</a>], (ii) inherently ill-posed in the Hadamard sense [<a href="#B23-ijgi-07-00457" class="html-bibr">23</a>,<a href="#B75-ijgi-07-00457" class="html-bibr">75</a>,<a href="#B117-ijgi-07-00457" class="html-bibr">117</a>], because affected by: (I) a 4D-to-2D data dimensionality reduction from the 4D geospatial-temporal scene-domain to the (2D, planar) image-domain, e.g., responsible of occlusion phenomena, and (II) a semantic information gap from ever-varying sub-symbolic sensory data (sensations) in the physical world to stable symbolic percepts in the mental model of the physical world (modeled world, world ontology, real-world model) [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>,<a href="#B19-ijgi-07-00457" class="html-bibr">19</a>,<a href="#B20-ijgi-07-00457" class="html-bibr">20</a>,<a href="#B21-ijgi-07-00457" class="html-bibr">21</a>,<a href="#B22-ijgi-07-00457" class="html-bibr">22</a>,<a href="#B23-ijgi-07-00457" class="html-bibr">23</a>,<a href="#B24-ijgi-07-00457" class="html-bibr">24</a>]. Since it is inherently ill-posed, vision requires <span class="html-italic">a priori</span> knowledge in addition to sensory data to become better posed for numerical solution [<a href="#B32-ijgi-07-00457" class="html-bibr">32</a>,<a href="#B33-ijgi-07-00457" class="html-bibr">33</a>]. If the aforementioned working hypothesis holds true, then the complexity of SCBIR + SEIKD is not inferior to the complexity of vision, acknowledged to be inherently ill-posed and NP-hard. To make the inherently-ill-posed CV problem better conditioned for numerical solution, a CV system is required to comply with human visual perception. In other words, a CV system is constrained to include a computational model of human vision [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B76-ijgi-07-00457" class="html-bibr">76</a>,<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B88-ijgi-07-00457" class="html-bibr">88</a>,<a href="#B89-ijgi-07-00457" class="html-bibr">89</a>,<a href="#B90-ijgi-07-00457" class="html-bibr">90</a>,<a href="#B91-ijgi-07-00457" class="html-bibr">91</a>,<a href="#B92-ijgi-07-00457" class="html-bibr">92</a>,<a href="#B93-ijgi-07-00457" class="html-bibr">93</a>,<a href="#B94-ijgi-07-00457" class="html-bibr">94</a>,<a href="#B95-ijgi-07-00457" class="html-bibr">95</a>,<a href="#B96-ijgi-07-00457" class="html-bibr">96</a>,<a href="#B97-ijgi-07-00457" class="html-bibr">97</a>,<a href="#B98-ijgi-07-00457" class="html-bibr">98</a>,<a href="#B99-ijgi-07-00457" class="html-bibr">99</a>,<a href="#B100-ijgi-07-00457" class="html-bibr">100</a>,<a href="#B101-ijgi-07-00457" class="html-bibr">101</a>,<a href="#B102-ijgi-07-00457" class="html-bibr">102</a>,<a href="#B103-ijgi-07-00457" class="html-bibr">103</a>,<a href="#B104-ijgi-07-00457" class="html-bibr">104</a>], i.e., ‘Human vision → CV’. Hence, dependence relationship: ‘Human vision → CV ⊃ EO-IU in operating mode ⊃ NASA EO Level 2 product → ESA EO Level 2 product → [EO-SCBIR + SEIKD = AI4DIAS] → GEO-GEOSS’ becomes our working hypothesis (to be duplicated in the body text). Equivalent to a first principle (axiom, postulate), This equation can be considered the first original contribution, conceptual in nature, of this research and technological development (RTD) study.</p>
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<p>Artificial intelligence (AI) for Data and Information Access Services (AI4DIAS), synonym for semantics-enabled DIAS or closed-loop EO image understanding (EO-IU) for semantic querying (EO-IU4SQ) system architecture. At the Marr level of system understanding known as system design (architecture) [<a href="#B76-ijgi-07-00457" class="html-bibr">76</a>], AI4DIAS is sketched as a closed-loop EO-IU4SQ system architecture, suitable for incremental semantic learning. It comprises a primary (dominant, necessary-but-not-sufficient) hybrid (combined deductive and inductive) feedback (provided with feedback loops) EO-IU subsystem in closed-loop with a secondary (dominated) hybrid feedback EO-SQ subsystem. <span class="html-italic">Subset-of</span> a computer vision (CV) system, where CV ⊃ EO-IU, the EO-IU subsystem is required to be automatic (no human–machine interaction is required by the CV system to run) and near real-time to provide the EO-SQ subsystem with useful information products, including thematic maps of symbolic quality, such as single-date ESA EO Level 2 Scene Classification Map (SCM) considered a necessary-but-not-sufficient pre-condition to semantic querying, synonym for semantics-enabled information/knowledge discovery (SEIKD) in massive multi-source EO image databases. The EO-SQ subsystem is provided with a graphic user interface (GUI) to streamline: (i) top-down knowledge transfer from-human-to-machine of an <span class="html-italic">a priori</span> mental model of the 4D geospatial-temporal real-world, (ii) high-level user- and application-specific EO semantic content-based image retrieval (SCBIR) operations. Output products generated by the closed-loop EO-IU4SQ system are expected to monotonically increase their value-added with closed-loop iterations, according to Bayesian updating where Bayesian inference is applied iteratively [<a href="#B122-ijgi-07-00457" class="html-bibr">122</a>,<a href="#B123-ijgi-07-00457" class="html-bibr">123</a>]: after observing some evidence, the resulting posterior probability can be treated as a prior probability and a new posterior probability computed from new evidence. One of Marr’s legacies is the notion of computational constraints required to make the typically ill-posed non-deterministic polynomial (NP)-hard problem of intelligence, encompassing vision [<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>], better conditioned for numerical solution [<a href="#B32-ijgi-07-00457" class="html-bibr">32</a>,<a href="#B33-ijgi-07-00457" class="html-bibr">33</a>]. Marr’s computational constraints reflecting properties of the world are embodied through evolution, equivalent to genotype [<a href="#B78-ijgi-07-00457" class="html-bibr">78</a>], into the human visual complex system, structured as a hierarchical network of networks with feedback loops [<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B88-ijgi-07-00457" class="html-bibr">88</a>,<a href="#B89-ijgi-07-00457" class="html-bibr">89</a>,<a href="#B90-ijgi-07-00457" class="html-bibr">90</a>,<a href="#B91-ijgi-07-00457" class="html-bibr">91</a>,<a href="#B92-ijgi-07-00457" class="html-bibr">92</a>,<a href="#B93-ijgi-07-00457" class="html-bibr">93</a>,<a href="#B96-ijgi-07-00457" class="html-bibr">96</a>,<a href="#B97-ijgi-07-00457" class="html-bibr">97</a>,<a href="#B98-ijgi-07-00457" class="html-bibr">98</a>]. Marr’s computational constraints are Bayesian priors in a Bayesian inference approach to vision [<a href="#B76-ijgi-07-00457" class="html-bibr">76</a>,<a href="#B122-ijgi-07-00457" class="html-bibr">122</a>], where ever-varying sensations (sensory data) are transformed into stable percepts (concepts) about the world in a world model [<a href="#B23-ijgi-07-00457" class="html-bibr">23</a>], to perform successfully in the world [<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>].</p>
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<p>Synonym for scene-from-image reconstruction and understanding, <span class="html-italic">vision</span> is a cognitive <span class="html-italic">(information-as-data-interpretation</span>) problem [<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>] very difficult to solve because: (i) non-deterministic polynomial (NP)-hard in computational complexity [<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B116-ijgi-07-00457" class="html-bibr">116</a>], and (ii) inherently ill-posed [<a href="#B23-ijgi-07-00457" class="html-bibr">23</a>,<a href="#B75-ijgi-07-00457" class="html-bibr">75</a>] in the Hadamard sense [<a href="#B117-ijgi-07-00457" class="html-bibr">117</a>]. <span class="html-italic">Vision</span> is inherently ill-posed because affected by: (I) a 4D-to-2D data dimensionality reduction from the 4D geospatial-temporal scene-domain to the (2D, planar) image-domain, e.g., responsible of occlusion phenomena, and (II) a semantic information gap from ever-varying sub-symbolic sensory data (sensations) in the physical world-domain to stable symbolic percepts in the mental model of the physical world (modeled world, world ontology, real-world model) [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B18-ijgi-07-00457" class="html-bibr">18</a>,<a href="#B19-ijgi-07-00457" class="html-bibr">19</a>,<a href="#B20-ijgi-07-00457" class="html-bibr">20</a>,<a href="#B21-ijgi-07-00457" class="html-bibr">21</a>,<a href="#B22-ijgi-07-00457" class="html-bibr">22</a>,<a href="#B23-ijgi-07-00457" class="html-bibr">23</a>,<a href="#B24-ijgi-07-00457" class="html-bibr">24</a>]. Since it is inherently ill-posed, <span class="html-italic">vision</span> requires <span class="html-italic">a priori</span> knowledge in addition to sensory data to become better posed for numerical solution [<a href="#B32-ijgi-07-00457" class="html-bibr">32</a>,<a href="#B33-ijgi-07-00457" class="html-bibr">33</a>].</p>
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<p>Semantics-enabled EO <span class="html-italic">big data cube</span>, synonym for artificial intelligence (AI) for Data and Information Access Services (AI4DIAS). Each single-date EO Level 1 source image, radiometrically calibrated into top-of-atmosphere reflectance (TOARF) values and stored in the database, is automatically transformed into an ESA EO Level 2 product comprising: (i) a single-date multi-spectral (MS) image radiometrically calibrated from TOARF into surface reflectance (SURF) values, corrected for atmospheric, adjacency and topographic effects, stacked with (ii) its EO data-derived value-adding scene classification map (SCM), equivalent to a sensory data-derived categorical/nominal/qualitative variable of semantic quality, where the thematic map legend is general-purpose, user- and application-independent and comprises quality layers, such as cloud and cloud–shadow. It is eventually stacked with (iii) its EO data-derived value-adding numeric variables, such as biophysical variables, e.g., leaf area index (LAI) [<a href="#B2-ijgi-07-00457" class="html-bibr">2</a>,<a href="#B131-ijgi-07-00457" class="html-bibr">131</a>], class-conditional spectral indexes, e.g., vegetation class-conditional greenness index [<a href="#B132-ijgi-07-00457" class="html-bibr">132</a>,<a href="#B133-ijgi-07-00457" class="html-bibr">133</a>], categorical variables of sub-symbolic quality (geographic field-objects), e.g., fuzzy sets/discretization levels low/medium/high of a numeric variable, etc. [<a href="#B134-ijgi-07-00457" class="html-bibr">134</a>].</p>
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<p>Definitions adopted in the notion of Space Economy 4.0: space segment, ground segment for «mission control» = upstream, ground segment for «user support» = midstream (infrastructures and services), downstream utility of space technology [<a href="#B66-ijgi-07-00457" class="html-bibr">66</a>] (pp. 6, 57). Cable of transforming quantitative (unequivocal) <span class="html-italic">big data</span> into qualitative (equivocal) data-derived value-adding information and knowledge, AI technologies should be applied as early as possible to the “seamless innovation chain” needed for a new era of Space 4.0, starting from AI4Space applications at the space segment, which include the notion of future intelligent EO satellites (FIEOS) [<a href="#B144-ijgi-07-00457" class="html-bibr">144</a>,<a href="#B145-ijgi-07-00457" class="html-bibr">145</a>], and AI4DIAS applications at midstream, such as systematic ESA EO Level 2 product generation, considered synonym for Analysis Ready Data (ARD) eligible for use at downstream.</p>
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<p>Mach bands illusion [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B156-ijgi-07-00457" class="html-bibr">156</a>]. In black: Ramp in luminance units across space. In red: Brightness (perceived luminance) across space. One of the best-known brightness illusions, where brightness is defined as a subjective aspect of vision, i.e., brightness is the perceived luminance of a surface, is the psychophysical phenomenon of the Mach bands: where a luminance (radiance, intensity) ramp meets a plateau, there are spikes of brightness, although there is no discontinuity in the luminance profile. Hence, human vision detects two boundaries, one at the beginning and one at the end of the ramp in luminance. Since there is no discontinuity in luminance where brightness is spiking, the Mach bands effect is called a visual “illusion”. Along a ramp, no image-contour is perceived by human vision, irrespective of the ramp’s local contrast (gradient) in range (0, +∞). In the words of Pessoa, “if we require that a brightness model should at least be able to predict Mach bands, the bright and dark bands which are seen at ramp edges, the number of published models is surprisingly small” [<a href="#B156-ijgi-07-00457" class="html-bibr">156</a>]. In 2D signal (image) processing, the important lesson to be learned from the Mach bands illusion is that local variance, contrast and first-order derivative (gradient) are statistical features (data-derived numeric variables) computed locally in the (2D) image-domain not suitable to detect image-objects (segments, closed contours) required to be perceptually “uniform” (“homogeneous”) in agreement with human vision. In other words, <span class="html-italic">these popular local statistics, namely, local variance, contrast and first-order derivative (gradient), are not suitable visual features if detected image-segments/image-contours are required to be consistent with human visual perception, including ramp-edge detection</span>. This straightforward (obvious), but not trivial observation is at odd with a large portion of the existing computer vision (CV) and remote sensing (RS) literature, where many semi-automatic image segmentation/image-contour detection algorithms are based on thresholding the local variance, contrast or first-order gradient, e.g., [<a href="#B157-ijgi-07-00457" class="html-bibr">157</a>,<a href="#B158-ijgi-07-00457" class="html-bibr">158</a>,<a href="#B159-ijgi-07-00457" class="html-bibr">159</a>], where a system’s free-parameter for thresholding image-objects or image-contours must be user-defined in range ∈ (0, +∞) based on heuristics.</p>
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<p>As in [<a href="#B74-ijgi-07-00457" class="html-bibr">74</a>], courtesy of Daniel Schläpfer, ReSe Applications Schläpfer. A complete (“augmented”) hybrid (combined deductive and inductive) inference workflow for multi-spectral (MS) image correction from atmospheric, adjacency and topographic effects. It combines a standard Atmospheric/Topographic Correction for Satellite Imagery (ATCOR) commercial software workflow [<a href="#B71-ijgi-07-00457" class="html-bibr">71</a>,<a href="#B72-ijgi-07-00457" class="html-bibr">72</a>], with a bidirectional reflectance distribution function (BRDF) effect correction, which requires as input an image time-series of the same surface area acquired with different combinations of the sun and sensor positions. Processing blocks are represented as circles and output products as rectangles. This hybrid workflow alternates deductive/prior knowledge-based and inductive/learning-from-data inference units, starting from initial conditions provided by a first-stage prior knowledge-based decision tree for static (non-adaptive to data) color naming, such as the Spectral Classification of surface reflectance signatures (SPECL) decision tree [<a href="#B73-ijgi-07-00457" class="html-bibr">73</a>] implemented within the ATCOR commercial software toolbox. Categorical variables generated as output by the two processing blocks identified as “pre-classification” and “classification” are employed as input by the subsequent processing blocks to stratify (mask) unconditional numeric variable distributions, in line with the statistic stratification principle [<a href="#B152-ijgi-07-00457" class="html-bibr">152</a>]. Through statistic stratification, inherently ill-posed inductive learning-from-data algorithms are provided with <span class="html-italic">a priori</span> knowledge required in addition to data to become better posed for numerical solution, in agreement with the machine learning-from-data literature [<a href="#B32-ijgi-07-00457" class="html-bibr">32</a>,<a href="#B33-ijgi-07-00457" class="html-bibr">33</a>].</p>
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<p>Sen2Cor flow chart for ESA Level 2 product generation from Sentinel-2 imagery [<a href="#B11-ijgi-07-00457" class="html-bibr">11</a>,<a href="#B12-ijgi-07-00457" class="html-bibr">12</a>,<a href="#B44-ijgi-07-00457" class="html-bibr">44</a>], same as in the Atmospheric/Topographic Correction for Satellite Imagery (ATCOR) commercial software toolbox [<a href="#B71-ijgi-07-00457" class="html-bibr">71</a>,<a href="#B72-ijgi-07-00457" class="html-bibr">72</a>,<a href="#B73-ijgi-07-00457" class="html-bibr">73</a>]. While sharing the same system design, ESA Sen2Cor and ATCOR differ at the two lowest levels of abstraction, known as algorithm and implementation [<a href="#B76-ijgi-07-00457" class="html-bibr">76</a>] (refer to <a href="#sec1-ijgi-07-00457" class="html-sec">Section 1</a>). First, a scene classification map (SCM) is generated from top-of-atmosphere reflectance (TOARF) values. Next, class-conditional MS image radiometric enhancement of TOARF into surface reflectance (SURF) values, synonym for bottom-of-atmosphere (BOA) reflectance values, corrected for atmospheric, adjacency and topographic effects is accomplished in sequence, stratified by the same SCM product generated at first stage from TOARF values. More acronyms in this figure: AOT = aerosol optical thickness, DEM = digital elevation model, LUT = look-up table.</p>
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<p>Ideal ESA EO Level 2 product generation design as a hierarchical alternating sequence of: (A) hybrid (combined deductive and inductive) radiometric enhancement of multi-spectral (MS) dimensionless digital numbers (DNs) into top-of-atmosphere reflectance (TOARF), surface reflectance (SURF) values and spectral albedo values corrected in sequence for (1) atmospheric, (2) adjacency, (3) topographic and (4) BRDF effects, and (B) hybrid (combined deductive and inductive) classification of TOARF, SURF and spectral albedo values into a sequence of ESA EO Level 2 scene classification maps (SCMs), whose legend (taxonomy) of community-agreed land cover (LC) class names, in addition to quality layers cloud and cloud–shadow, increases hierarchically in semantics and mapping accuracy. An implementation in operating mode of this EO image pre-processing system design for stratified topographic correction (STRATCOR) is presented and discussed in [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B82-ijgi-07-00457" class="html-bibr">82</a>,<a href="#B83-ijgi-07-00457" class="html-bibr">83</a>,<a href="#B107-ijgi-07-00457" class="html-bibr">107</a>]. In comparison with this desirable system design, let us consider that, for example, the existing Sen2Cor software toolbox, developed by ESA to support a Sentinel-2 sensor-specific Level 2 product generation on the user side [<a href="#B11-ijgi-07-00457" class="html-bibr">11</a>,<a href="#B12-ijgi-07-00457" class="html-bibr">12</a>,<a href="#B44-ijgi-07-00457" class="html-bibr">44</a>], adopts no hierarchical alternating approach between MS image classification and MS image radiometric enhancement. Rather, ESA Sen2Cor accomplishes, first, one SCM generation from TOARF values based on a per-pixel (spatial context-insensitive) prior spectral knowledge-based decision tree. Next, a class-conditional MS image radiometric enhancement of TOARF into SURF values corrected for atmospheric, adjacency and topographic effects is accomplished in sequence, stratified by the same SCM product generated at first stage from TOARF values, see <a href="#ijgi-07-00457-f011" class="html-fig">Figure 11</a>.</p>
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<p>Cloud classification according to the U.S. National Weather Service adapted from [<a href="#B164-ijgi-07-00457" class="html-bibr">164</a>].</p>
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<p>Adapted from [<a href="#B55-ijgi-07-00457" class="html-bibr">55</a>]. Sun-cloud-satellite geometry for arbitrary viewing and illumination conditions. <b>Left</b>: Actual 3D representation of the Sun/cloud/cloud–shadow geometry. Cloud height, <span class="html-italic">h</span>, is a typical unknown variable. Right: Apparent Sun/cloud/cloud–shadow geometry in a 2D soil projection, with <b><span class="html-italic">a<sub>g</sub></span></b> = <b><span class="html-italic">h</span></b> ⋅ tanφ<sub>β</sub>, <b><span class="html-italic">b<sub>g</sub></span></b> = <b><span class="html-italic">h</span></b> ⋅ tanφ<sub>μ</sub>.</p>
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<p>Example of 1D image analysis, which is spatial topology non-preserving (non-retinotopic) in a (2D) image-domain [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B88-ijgi-07-00457" class="html-bibr">88</a>,<a href="#B96-ijgi-07-00457" class="html-bibr">96</a>,<a href="#B170-ijgi-07-00457" class="html-bibr">170</a>]. Intuitively, 1D image analysis is insensitive to permutations in the input data set [<a href="#B34-ijgi-07-00457" class="html-bibr">34</a>]. Synonym for 1D analysis of a 2D gridded data set, 1D image analysis is affected by spatial data dimensionality reduction. The (2D) image at left is transformed into the 1D vector data stream (sequence) shown at bottom, where vector data are either pixel-based or spatial context-sensitive, e.g., local window-based. This 1D vector data stream means nothing to a human photo interpreter. When it is input to either an inductive learning-from-data classifier or a deductive learning-by-rule classifier, the 1D vector data sequence is what the classifier actually sees when watching the (2D) image at left. Undoubtedly, computers are more successful than humans in 1D image analysis. Nonetheless, humans are still far more successful than computers in 2D image analysis, which is spatial context-sensitive and spatial topology-preserving (retinotopic) (see <a href="#ijgi-07-00457-f016" class="html-fig">Figure 16</a>).</p>
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<p>2D image analysis is synonym for spatial context-sensitive and spatial topology-preserving (retinotopic) feature mapping in a (2D) image-domain [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B87-ijgi-07-00457" class="html-bibr">87</a>,<a href="#B88-ijgi-07-00457" class="html-bibr">88</a>,<a href="#B96-ijgi-07-00457" class="html-bibr">96</a>,<a href="#B170-ijgi-07-00457" class="html-bibr">170</a>]. Intuitively, 2D image analysis is sensitive to permutations in the input data set [<a href="#B34-ijgi-07-00457" class="html-bibr">34</a>]. Activation domains of physically adjacent processing units in the 2D array of convolutional spatial filters are spatially adjacent regions in the 2D visual field. Provided with a superior degree of biological plausibility in modelling 2D spatial topological and spatial non-topological information components, distributed processing systems capable of 2D image analysis, such as deep convolutional neural networks (DCNNs), typically outperform traditional 1D image analysis approaches. Will computers ever become as good as humans in 2D image analysis?</p>
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<p>EO for Geographical Sciences (EO4GEO, EO4GIScience) framework, meaning EO big data analytics in operating mode for GIScience applications, constrained by 2D (retinotopic, spatial topology-preserving) image analysis in cognitive science [<a href="#B129-ijgi-07-00457" class="html-bibr">129</a>]. EO4GEO is more restrictive than the traditional GEOBIA paradigm, formalized in 2006 and 2014 as a viable alternative to 1D spatial context-insensitive (pixel-based) image analysis [<a href="#B9-ijgi-07-00457" class="html-bibr">9</a>,<a href="#B10-ijgi-07-00457" class="html-bibr">10</a>,<a href="#B130-ijgi-07-00457" class="html-bibr">130</a>].</p>
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<p>Examples of land cover (LC) class-specific families of spectral signatures [<a href="#B17-ijgi-07-00457" class="html-bibr">17</a>] in top-of-atmosphere reflectance (TOARF) values, which include surface reflectance (SURF) values as a special case in clear sky and flat terrain conditions [<a href="#B173-ijgi-07-00457" class="html-bibr">173</a>], i.e., in general, TOARF ⊇ SURF, where TOARF ≈ SURF (depicted as an ideal “noiseless” spectral signature in red) + atmospheric and topographic noise. A within-class family of spectral signatures (e.g., dark-toned soil) in TOARF or SURF values forms a buffer zone (hyperpolyhedron, envelope, manifold, joint distribution), depicted in light green. Like a vector quantity has two characteristics, a magnitude and a direction, any LC class-specific MS manifold is characterized by a multivariate shape and a multivariate intensity information component. In the RS literature, typical prior knowledge-based spectral decision trees for MS reflectance space hyperpolyhedralization into a finite and discrete vocabulary of MS color names, such as Sen2Cor’s [<a href="#B12-ijgi-07-00457" class="html-bibr">12</a>], MAJA’s [<a href="#B46-ijgi-07-00457" class="html-bibr">46</a>,<a href="#B48-ijgi-07-00457" class="html-bibr">48</a>], ATCOR’s [<a href="#B71-ijgi-07-00457" class="html-bibr">71</a>,<a href="#B72-ijgi-07-00457" class="html-bibr">72</a>], LEDAPS’ [<a href="#B139-ijgi-07-00457" class="html-bibr">139</a>,<a href="#B140-ijgi-07-00457" class="html-bibr">140</a>,<a href="#B146-ijgi-07-00457" class="html-bibr">146</a>] and LaSRC’s [<a href="#B139-ijgi-07-00457" class="html-bibr">139</a>,<a href="#B140-ijgi-07-00457" class="html-bibr">140</a>,<a href="#B160-ijgi-07-00457" class="html-bibr">160</a>], typically adopt either a multivariate analysis of spectral indexes or a logical (AND, OR) combination of univariate variables, such as scalar spectral indexes or spectral channels, considered mutually independent. A typical spectral index is a scalar band ratio or band-pair difference equivalent to an angular coefficient of a tangent to the spectral signature in one point. It is well known that infinite functions can feature the same tangent value in one point. In practice, no spectral index or combination of spectral indexes can reconstruct the multivariate shape and multivariate intensity information components of a spectral signature. As a viable alternative to traditional static (non-adaptive to data) spectral rule-based decision trees found in the RS literature, the Satellite Image Automatic Mapper (SIAM)’s prior knowledge-based spectral decision tree [<a href="#B13-ijgi-07-00457" class="html-bibr">13</a>,<a href="#B14-ijgi-07-00457" class="html-bibr">14</a>,<a href="#B15-ijgi-07-00457" class="html-bibr">15</a>,<a href="#B82-ijgi-07-00457" class="html-bibr">82</a>,<a href="#B83-ijgi-07-00457" class="html-bibr">83</a>,<a href="#B107-ijgi-07-00457" class="html-bibr">107</a>,<a href="#B118-ijgi-07-00457" class="html-bibr">118</a>,<a href="#B132-ijgi-07-00457" class="html-bibr">132</a>,<a href="#B133-ijgi-07-00457" class="html-bibr">133</a>,<a href="#B161-ijgi-07-00457" class="html-bibr">161</a>,<a href="#B162-ijgi-07-00457" class="html-bibr">162</a>,<a href="#B174-ijgi-07-00457" class="html-bibr">174</a>] adopts a convergence-of-evidence approach to model any target family (ensemble) of spectral signatures, forming a hypervolume of interest in the MS reflectance hyperspace, as a combination of multivariate shape information with multivariate intensity information components. For example, as shown above, typical spectral signatures of dark-toned soils and typical spectral signatures of light-toned soils form two MS envelopes in the MS reflectance hyperspace that approximately share the same multivariate shape information component, but whose pair of multivariate intensity information components does differ.</p>
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<p>Adapted from [<a href="#B172-ijgi-07-00457" class="html-bibr">172</a>]. Unlike a MS reflectance space hyperpolyhedralization difficult to think of and impossible to visualize when the number of channels is superior to three, an RGB data cube polyhedralization is intuitive to think of and straightforward to display. For example, based on psychophysical evidence, human basic color (BC) names can be mapped onto a monitor-typical RGB data cube. Central to this consideration is Berlin and Kay’s landmark study of a “universal” inventory of eleven BC words in twenty human languages: black, white, gray, red, orange, yellow, green, blue, purple, pink and brown [<a href="#B171-ijgi-07-00457" class="html-bibr">171</a>].</p>
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