International audience

Artificial intelligence has become pervasive across disciplines and fields, and biomedical image and signal processing is no exception. The growing and widespread interest on the topic has triggered a vast research activity that is reflected in an exponential research effort. Through study of massive and diverse biomedical data, machine and deep learning models have revolutionized various tasks such as modeling, segmentation, registration, classification and synthesis, outperforming traditional techniques. However, the difficulty in translating the results into biologically/clinically interpretable information is preventing their full exploitation in the field. Explainable AI (XAI) attempts to fill this translational gap by providing means to make the models interpretable and providing explanations. Different solutions have been proposed so far and are gaining increasing interest from the community. This paper aims at providing an overview on XAI in biomedical data processing and points to an upcoming Special Issue on Deep Learning in Biomedical Image and Signal Processing of the IEEE Signal Processing Magazine that is going to appear in March 2022.

International audience

Texture characterization from the metrological point of view is addressed in order to establish a physically relevant and directly interpretable feature. In this regard, a generic formulation is proposed to simultaneously capture the spectral and spatial complexity in hyperspectral images. The feature, named relative spectral difference occurrence matrix (RSDOM) is thus constructed in a multireference, multidirectional, and multiscale context. As validation, its performance is assessed in three versatile tasks. In texture classification on HyTexiLa, content-based image retrieval (CBIR) on ICONES-HSI, and land cover classification on Salinas, RSDOM registers 98.5% accuracy, 80.3% precision (for the top 10 retrieved images), and 96.0% accuracy (after post-processing) respectively, outcompeting GLCM, Gabor filter, LBP, SVM, CCF, CNN, and GCN. Analysis shows the advantage of RSDOM in terms of feature size (a mere 126, 30, and 20 scalars using GMM in order of the three tasks) as well as metrological validity in texture representation regardless of the spectral range, resolution, and number of bands.

In this paper, we propose a saliency-weighted stereoscopic JND (SSJND) model constructed based on psychophysical experiments, accounting for binocular disparity and spatial masking effects of the human visual system (HVS). Specifically, a disparity-aware binocular JND model is first developed using psychophysical data, and then is employed to estimate the JND threshold for non-occluded pixel (NOP). In addition, to derive a reliable 3D-JND prediction, we determine the visibility threshold for occluded pixel (OP) by including a robust 2D-JND model. Finally, SSJND thresholds of one view are obtained by weighting the resulting JND for NOP and OP with their visual saliency. Based on subjective experiments, we demonstrate that the proposed model outperforms the other 3D-JND models in terms of perceptual quality at the same noise level.

A new hyperspectral texture descriptor, Relocated Spectral Difference Occurrence Matrix (rSDOM) is proposed. It assesses the distribution of spectral difference in a given neighborhood. For metrological purposes, rSDOM employs Kullback-Leibler pseudo-divergence (KLPD) for spectral difference calculation. It is generic and adapted for any spectral range and number of band. As validation, a texture classification scheme based on nearest neighbor classifier is applied on HyTexiLa dataset using rSDOM. The performance is close to Opponent Band Local Binary Pattern (OBLBP) with classification accuracy of 94.7%, but at a much-reduced feature size (0.24% of OBLBP's) and computational complexity.

Gradient extraction is important for a lot of metrological applications such as Control Quality by Vision. In this work, we propose a full-vector gradient for multi-spectral sensors. The full-vector gradient extends Di Zenzo expression to take into account the non-orthogonality of the acquisition channels thanks to a Gram matrix. This expression is generic and independent from channel count. Results are provided for a color and a multi-spectral snapshot sensor. Then, we show the accuracy improvement of the gradient calculation by creating a dedicated objective test and from real images.

In this paper, we study the importance of spectral sensitivity functions in constructing discriminative representation of hyperspectral images (HSI). The main goal of a such representation is to improve image content recognition by focusing the processing only on the most relevant spectral channels. The underlying hypothesis is that for a given category, each image content is better extracted through a specific set of spectral sensitivity functions. In this study, we fixed the number of spectral sensitivity functions to 3 for displaying purposes. Deep features are then extracted from the obtained trichromatic representation of HSI data to build a discriminative image signature. Finally, spectral sensitivity functions are compared in a Content-Based Image Retrieval (CBIR) paradigm. Exhaustive experiments have been conducted on a hyperspectral dataset. Obtained results show the usefulness of the whole spectrum to obtain a discriminative image representation compared to the RGB representation.

No-reference (NR) stereoscopic 3D (S3D) image quality assessment (SIQA) is still challenging due to the poor understanding of how the human visual system (HVS) judges image quality based on binocular vision. In this paper, we propose an efficient opinion-aware NR Stereoscopic Quality predictor based on local contrast statistics combination (SQSC). Specifically, for left and right views, we first extract statistical features of the gradient magnitude (GM) and Laplacian of Gaussian (LoG) responses, describing the image local structures from different perspectives. The HVS is insensitive to low-order statistical redundancies that can be removed by LoG filtering. Hence, the monocular statistical features are then fused to derive the binocular features based on a linear combination model using LoG responses-based weightings. These weightings can efficiently simulate the binocular rivalry (BR) phenomenon. Finally, the binocular features and the subjective scores were jointly employed to construct a learned regression model obtained by the support vector regression (SVR) algorithm. Experimental results on three widely used 3D IQA databases demonstrate the high prediction performance of the proposed method when compared to recent well performing SIQA methods.

One of the most challenging issues in stereoscopic image quality assessment (IQA) is how to effectively model the binocular behaviors of the human visual system (HVS). The latter has a great impact on the perceptual stereoscopic 3D (S3D) quality. This paper presents a stereoscopic IQA metric based on the properties of the HVS. Instead of measuring the quality of the left and the right views separately, the proposed method predicts the quality of a cyclopean image to ensure that the overall S3D quality is as close as possible to the binocular vision. The cyclopean image is synthesized based on the local entropy of each view with the aim to simulate the phenomena of the binocular rivalry/suppression. A 2D IQA metric is employed to assess the quality of both the cyclopean image and the disparity map. Additionally, the quality of the cyclopean image is modulated according to the visual importance of each pixel defined by the just noticeable difference (JND). Finally, the 3D quality score is derived by combining the quality estimates of the cyclopean image and disparity map. Experimental results show that the proposed method outperforms many other state-of-the-art SIQA methods in terms of prediction accuracy and computational efficiency.

One of the most challenging issues in stereoscopic image quality assessment (SIQA) is how to effectively model the binocular behavior of the human visual system (HVS). The latter has a great impact on the perceptual 3D quality. In this paper, we propose a SIQA metric accounting for binocular combination properties and disparity information. Instead of computing the quality of the left and the right views separately, the proposed metric predicts the quality of a cyclopean image so as to have a good consistency with 3D human perception. The cyclopean image is synthesized based on the local entropy and the visual saliency of each view with the aim to simulate the phenomena of binocular fusion/rivalry. A 2D IQA metric is employed to assess the quality of both the cyclopean image and the disparity map. The obtained scores are used to derive the 3D quality score thanks to a pooling stage. Experimental results on three public 3D IQA databases show that the proposed method outperforms many other state-of-the-art SIQA methods, and achieves high prediction accuracy on these databases.

Automatic or semi-automatic stereoscopic image quality assessment has arisen due to the recent diffusion of a new generation of stereoscopic technologies and content demand. Thereby, there is a growth in asking for algorithms of Stereoscopic Image Quality Metrics (SIQA). In this paper, we present a method for assessing the stereoscopic image quality, QUALITAS. QUALITAS is grounded on some human visual system features such as contrast sensitivity, effect of disparate image quality in left and right images, and distance perception, which do not depend on the images being tested. QUALITAS is defined in five stages. Instead of averaging individual qualities of the stereo-pair, QUALITAS introduces Contrast Band-Pass Filtering on a wavelet domain at both views, namely our algorithm perceptually weights left and right images depending on certain viewing conditions. This paper includes the comparison of 27 Metrics SIQA proposed by 16 authors, which summarizes the work made in this field in the recent five years, on image database LIVE 3D. Some algorithms can be combined with any 2D/Normal Image Quality Assessments (NIQA), giving as a result that QUALITAS was compared against 221 Metrics. QUALITAS obtained the best results in terms of overall performance of correlation coefficients. We conclude all metrics in SIQA-SET are simple modifications of NIQA, which take into account some extra characteristics from the disparity map (usually depth variances). Instead QUALITAS incorporates disparity masking in addition to divide 3D scenario in two parts: background and foreground planes. Moreover QUALITAS employs a contrast band-pass filtering, so dynamic parameters are considered as observational distance. It includes loss of correlation, luminance and contrast distortion. It takes into account the visual differences between left and right images, employing a penalization depending on their wavelet energy. Thus, the novelty of QUALITAS lies in combining some the best features of stereoscopic image quality assessments.

The just noticeable difference (JND) notion reflects the maximum tolerable distortion. It has been extensively used for the optimization of 2D applications. For stereoscopic 3D (S3D) content, this notion is different since it relies on different mechanisms linked to our binocular vision. Unlike 2D, 3D-JND models appeared recently and the related literature is rather limited. These models can be used for the sake of compression and quality assessment improvement for S3D content. In this paper, we propose a deep and comparative study of the existing 3D-JND models. Additionally, in order to analyze their performance, the 3D-JND models have been integrated in recent metric dedicated to stereoscopic image quality assessment (SIQA). The results are reported on two widely used S3D image databases.

A great deal of features detectors and descriptors are proposed every years for several computer vision applications. In this paper, we concentrate on dense detector applied to different descriptors. Eight descriptors are compared, three from gradient based family (SIFT, SURF, DAISY), others from binary category (BRIEF, ORB, BRISK, FREAK and LATCH). These descriptors are created and defined with certain invariance properties. We want to verify their invariances with various geometric and photometric transformations, varying one at a time. Deformations are computed from an original image. Descriptors are tested on five transformations: scale, rotation, viewpoint, illumination plus reflection. Overall, descriptors display the right invariances. This paper's objective is to establish a reproducible protocol to test descriptors invariances.

Automatic or semi-automatic stereoscopic image quality assessment has arisen due to the recent diffusion of a new generation of stereoscopic technologies and content demand. Thereby, there is a growth in asking for algorithms of Stereoscopic Image Quality Metrics (SIQA). In this paper, we present a method for assessing the stereoscopic image quality, QUALITAS. QUALITAS is grounded on some human visual system features such as contrast sensitivity, effect of disparate image quality in left and right images, and distance perception, which do not depend on the images being tested. QUALITAS is defined in five stages. Instead of averaging individual qualities of the stereo-pair, QUALITAS introduces Contrast Band-Pass Filtering on a wavelet domain at both views, namely our algorithm perceptually weights left and right images depending on certain viewing conditions. This paper includes the comparison of 27 Metrics SIQA proposed by 16 authors, which summarizes the work made in this field in the recent five years, on image database LIVE 3D. Some algorithms can be combined with any 2D/Normal Image Quality Assessments (NIQA), giving as a result that QUALITAS was compared against 221 Metrics. QUALITAS obtained the best results in terms of overall performance of correlation coefficients. We conclude all metrics in SIQA-? are simple modifications of NIQA, which take into account some extra characteristics from the disparity map (usually depth variances). Instead QUALITAS incorporates disparity masking in addition to divide 3D scenario in two parts: background and foreground planes. Moreover QUALITAS employs a contrast band-pass filtering, so dynamic parameters are considered as observational distance. It includes loss of correlation, luminance and contrast distortion. It takes into account the visual differences between left and right images, employing a penalization depending on their wavelet energy. Thus, the novelty of QUALITAS lies in combining some the best features of stereoscopic image quality assessments.

Splicing operation is a common technique used for image forgery. In this paper, we propose a new method for detecting the image splicing by revealing inconsistencies of the illuminant color in the object regions. For this, we first divide a given image into some horizontal and vertical bands. After that, the illuminant of each band is estimated with the generalized grey-world algorithms. For each illuminant estimation algorithm, the fake patches produced by computing the intersection between the forged horizontal and vertical bands are represented in a forgery detection map. Finally the spliced regions are shown by combining all splicing detection maps. Our proposed method is validated with several test cases. Additionally, we compare the performance of our method with two existing methods on the dataset CASIA V2.0. The results show that the proposed method works well with minimal human interaction.

Content Based Image Retrieval (CBIR) systems retrieve the most similar images to a query image in a collection. One of the most popular models and widely applied in this task is the Bag of Visual Words model (BoVW). In this paper, we introduce an evaluation study of different information gain models used for the construction of a visual word vocabulary. In the proposed framework, the information gain is used as discriminative information to index image features and select the ones that have the highest values of information gain. The empirical experiments made for this study evaluate the effect of four different information gain models: tf-idf, entropy, bm25, tfc with respect to different descriptors and image databases. The results show that selecting the image features based on at least one of the studied information gain model allows the retrieval process to be more accurate than the classical Bag of Visual Words model.

Saliency is one of the most important features in human visual perception. It is widely used nowadays for perceptually optimizing image processing algorithms. Several models have been proposed for 2D images and only few attempts can be observed for 3D ones. In this paper, we propose a stereoscopic 3D saliency model relying on 2D saliency features jointly with depth obtained from monocular cues. On the one hand, the use of 2D saliency features is justified psychophysically by the similarity observed between 2D and 3D attention maps. On the other hand, 3D perception is significantly based on monocular cues. The validation of our model using state-of-the-art procedures including Kullback-Leibler divergence (KLD), area under the curve (AUC) and correlation coefficient (CC) in comparison with attention maps showed very good performance.

Modeling visual attention is an important stage for the optimization of image processing systems nowadays. Several models have been already developed for 2D static and dynamic content, but only few attempts can be found for stereoscopic 3D content. In this work we propose a saliency model for stereoscopic 3D video. This model is based the fusion of three maps i.e. spatial, temporal and depth. It relies on interest point features known for being close to human visual attention. Moreover, since 3D perception is mostly based on monocular cues, depth information is obtained using a monocular model predicting the depth position of objects. Several fusion strategies have been experimented in order to determine the best match for our model. Finally, our approach has been validated using state-of-the-art metrics in comparison to attention maps obtained by eye-tracking experiments, and showed good performance.

Facing the increasing number of multi and hyperspectral image acquisitions, in particular for medical and industrial applications, we need accurate features to analyse and assess the content complexity in a metrological way. In this paper, we explore an original way to compute texture features for spectral images in a full-band and vector process. To do it, we developed a dedicated approach for Mathematical Morphology using distance function. Thanks to this, we extend the classical mathematical morphology to spectral images. We show in this paper the scientific construction and preliminary results.

In content based image retrieval, one of the most important step is the construction of image signatures. To do so, a part of state-of-the-art approaches propose to build a visual vocabulary. In this paper, we propose a new methodology for visual vocabulary construction that obtains high retrieval results. Moreover, it is computationally inexpensive to build and needs no prior knowledge on features or dataset used.

The aim of this work is to define a no-referenced perceptual image quality estimator applying the perceptual concepts of the Chromatic Induction Model. The approach consists in comparing the received image, presumably degraded, against the perceptual versions (different distances) of this image degraded by means of a Model of Chromatic Induction, which uses some of the human visual system properties. Also we compare our model with a original estimator in image quality assessment, PSNR. Results are highly correlated with the ones obtained by PSNR for image (99.32% Lenna and 96.95% for image Baboon), but this proposal does not need an original image or a reference one in order to give an estimation of the quality of the degraded image.

This work describes a perceptual method (pGBbBShift) for coding of Region of Interest (ROI) areas. It introduces perceptual criteria to the pGBbBShift method when bit planes of ROI and background areas are shifted. This additional feature is intended for balancing perceptual importance of some coefficients regardless their numerical importance. Perceptual criteria are applied using the CIWaM, which is a low-level computational model that reproduces color perception in the Human Visual System. Results show that there is no perceptual difference at ROI between the MaxShift method and pGBbBShift and, at the same time, perceptual quality of the entire image is improved when using pGBbBShift. Furthermore, when pGBbBShift method is applied to Hi-SET coder and it is compared against MaxShift method applied to both the JPEG2000 standard and the Hi-SET, the images coded by the combination pGBbBShift-Hi-SET get the best results when the overall perceptual image quality is estimated. The pGBbBShift method is a generalized algorithm that can be applied to other Wavelet based image compression algorithms such as JPEG2000, SPIHT or SPECK.

Monogenic wavelets offer a geometric representation of grayscale images through an AM-FM model allowing invariance of coefficients to translations and rotations. The underlying concept of local phase includes a fine contour analysis into a coherent unified framework. Starting from a link with structure tensors, we propose a nontrivial extension of the monogenic framework to vector-valued signals to carry out a nonmarginal color monogenic wavelet transform. We also give a practical study of this new wavelet transform in the contexts of sparse representations and invariant analysis, which helps to understand the physical interpretation of coefficients and validates the interest of our theoretical construction.

In the last decade, an important research effort has been dedicated to quality assessment from subjective and objective points of view. The focus was mainly on Full Reference (FR) metrics because of the ability to compare to an original. Only few works were oriented to Reduced Reference (RR) or No Reference (NR) metrics, very useful for applications where the original image is not available such as transmission or monitoring. In this work, we propose a RR metric based on two concepts, the interest points of the image and the objects saliency on color images. This metric needs a very low amount of data (lower than 8 bytes) to be able to compute the quality scores. The results show a high correlation between the metric scores and the human judgement and a better quality range than well-known metrics like PSNR or SSIM. Finally, interest points have shown that they can predict the quality of compressed color images.

We present model based approaches for colour texture characterization in IHLS colour space. Pure chrominance structure information is used in parallel with luminance structure information for colour texture classification. Hue and saturation channels are combined through a complex exponential to give a single channel which holds all the chrominance information of the image. Two dimensional complex multichannel versions of Non-Symmetric Half Plane Autoregressive model and Gauss Markov Random Field model are used to perform parametric power spectrum estimation of both luminance and the ldquocombined chrominancerdquo channels of the image. Colour texture classification is done using k-nearest neighbor algorithm on spectral distance measures both for luminance and chrominance channels individually as well as combined through a combination coefficient. Experimental results show that colour texture characterization obtained by combined luminance and chrominance structure informations is better than the one obtained by using only luminance structure information.

In this paper, a new image coding scheme based on a wavelet-like transform derived from orthogonal polynomial basis is presented. From a set of bivariate orthogonal polynomial functions, we first obtain the 2D non-separable wavelet functions to propose a wavelet-like transform coding. The motivation behind using orthogonal polynomials is that they exhibit some properties related to the human visual system (HVS). After applying the proposed transformation, the transform coefficients are threshold coded using quantization and bit allocation as in JPEG baseline system. The performance of the proposed transform coding is reported. The proposed coding scheme is also compared with other transform coding methods such as JPEG, JPEG 2000 and JPEG-XR/HDPHOTO.

It is well known that removing cloud-contaminated portions of a remotely sensed image and then filling in the missing data represent an important photo editing cumbersome task. In this paper, an efficient inpainting technique for the reconstruction of areas obscured by clouds or cloud shadows in remotely sensed images is presented. This technique is based on the Bandelet transform and the multiscale geometrical grouping. It consists of two steps. In the first step, the curves of geometric flow of different zones of the image are determined by using the Bandelet transform with multiscale grouping. This step allows an efficient representation of the multiscale geometry of the image's structures. Having well represented this geometry, the information inside the cloud-contaminated zone is synthesized by propagating the geometrical flow curves inside that zone. This step is accomplished by minimizing a functional whose role is to reconstruct the missing or cloud contaminated zone independently of the size and topology of the inpainting domain. The proposed technique is illustrated with some examples on processing aerial images. The obtained results are compared with those obtained by other clouds removal techniques.

With the multiplicity of imaging devices, the color quality and portability have become a very challenging problem. Moreover, a color is perceived with regards to its environment. So, if this environment changes it implies a change in the perceived color. In order to address this influence, the CIE (Commission Internationale de I'eclairage) has standardized a tool named color appearance model (CIECAM97*, CIECAM02). These models are able to take into account many phenomena related to human vision of color and can predict the color of a stimulus, function of its observations conditions. However, these models do not deal with the influence of spatial frequencies which can have a big impact on our perception. In this paper, we present an extended version of the CIECAM02 that integrates a spatial model correcting the color in relation to its spatial frequency. Moreover, the previous model has been modified to deal with images and not only single stimulus. The main difference with the rendering models (e.g. iCAM) lies in the fact that the proposed model, takes into account the spatial repartition of a pixel in addition to its environment. The obtained results are sound and demonstrate the efficiency of the proposed extension. This has been checked thanks to a psychophysical study where observers were assigned the task of assessing the quality of the improved version in comparison to the original.

A framework for active contour segmentation in vector-valued images is presented. It is known that the standard active contour is a powerful segmentation method, yet it is susceptible to weak edges and image noise. The proposed scheme uses foveal wavelets for an accurate detection of the edges singularities of the image. The foveal wavelets introduced by Mallat (2000) are known by their high capability to precisely characterize the holder regularity of singularities. Therefore, image contours are accurately localized and are well discriminated from noise. Foveal wavelet coefficients are updated using the gradient descent algorithm to guide the snake deformation to the true boundaries of the objects being segmented. Thus, the curve flow corresponding to the proposed active contour holds formal existence, uniqueness, stability and correctness results in spite of the presence of noise where traditional snake approach may fail.

Visual tasks often require a hierarchical representation of images in scales ranging from coarse to fine. A variety of linear and nonlinear smoothing techniques, such as Gaussian smoothing, anisotropic diffusion, regularization, wavelet thresholding etc... have been proposed. In this work, we propose a geometrical multiscale anisotropic diffusion based on the geometrical flow for denoising multivalued images. The geometrical flow is determined by the Bandelet transform of the image being processed. Consequently, the image is segmented into a quadtree where each square regroups pixels sharing the same geometrical flow direction. The motivation of this work is to introduce a new multiscale multistructure bandelet-based diffusion tensor to adjust the anisotropic diffusion toward the direction of the optimal geometrical flow. Therefore, multiple dyadic squares in the quadtree have multiple structure tensors. Hence, a more accurate geometrically driven noise suppression is obtained where the homogeneity of different image regions is well maintained.

In this paper, we propose a color image quantization algorithm based upon TBM. In this context, we consider that the color quantization problem can be viewed as clustering problem of the color-space into P clusters. Using TBM, we define a top-down evidential clustering algorithm which iteratively decreases the number of clusters of the color space into P clusters. This convergence is ensured using a novel criterion based upon the pignistic probability function. The P clusters provide the new reduced color palette and a quantized color image is computed. This quantization method is completely automatic and preserves the final result from any initial condition. Experiments on various images show the algorithm efficiency for color quantization and highlight the efficiency of TBM for color image processing

This article proposes a local photometric model that compensates for specular highlights and lighting variations due to position and intensity changes. We define clearly on which assumptions it is based, according to widely used reflection models. Moreover, its theoretical validity is studied according to few configurations of the scene geometry (lighting, camera and object relative locations). Next, this model is used to improve the robustness of points tracking in luminance images with respect to specular highlights and lighting changes.

Models of the human visual system are particularly interesting to quantify the quality of the display systems and to predict if visual information will be perceptible or not. One of these models is the contrast sensitivity function (CSF) which characterizes the sensitivity of the visual system to the spatial and temporal frequencies. The achromatic CSF can be measured, relatively, by a method of pairing which consists in matching the contrast of a test grid with that of a reference grid. To determine the reproducible grids on a screen, it is practical to use a frequency/observation distance diagram. The tests of this study are carried out under the conditions of medical diagnosis for radiographies with sinusoidal stimuli. The obtained results were approximated by a model in order to facilitate their integration in other models.

This paper introduces a new strategy to describe wavelet sub-bands in the scope of texture characterization. While most wavelet-based texture features found in the literature do not use spatial information contained in the wavelet domain, the new approach suggests to represent sub-bands of a texture by shape parameters. This new technique is called wavelet geometrical features (WGF), and is coming from a multiresolution extension of Chen's statistical geometrical features (SGF). Experiments on the full Brodatz database show the efficiency of the WGF over the SGF and the traditional wavelet energy signature.

The paper presents a watermarking technique, specific to color images. The insertion and the detection are based on the 2D discrete wavelet transform, applied on each color component. Three color vectors are extracted from the wavelet coefficients. The insertion consists of modifying one vector for each location, with regard to the bit value and the vector triplet. The mark is extracted without the original image, by observing the scheme of each vector triplet. This new method has been shown to be resistant to JPEG compression, median filtering and noise adding. Moreover, each insertion is weighted by an adaptive strength, obtained by a retroactive process between the original and the watermarked images. This process allows optimizing the compromise between invisibility and robustness, considering the local image color content.

In this article, we study the color appearance of the ink printed on a background, according to both its concentration and the background color. We find some attributes, the concentration quotients ratios, that are more invariant to the ink concentration than simple color attributes. Our work deals with traceability of porcine products. We have to detect the animal identifier, printed with ink on the pork rind. Using the concentration quotients ratios, our segmentation technique succeeds for any quantity of ink and any hue of pork rind. This technique could be applied to segment any set of pixels, that are colorimetrically and spatially close, but not necessarily all connected.

We propose a method to introduce spatial information within the context of pattern recognition by the mean of evidence theory. Indeed, we can consider that each neighbor brings some information useful to determined the class of a pattern to classify. We propose to introduce such information through the Dempster's (1967) combination rule. This combination, which takes into account the distance between neighbors, provides a more accurate modeling of the information and improves the classification process of the data. We illustrate the interest and the impact of this method through the problem of segmentation of multi-echo magnetic resonance (MR) images. In particular, we show that the segmentation results are more accurate and that some ambiguities of classification are resolved.

Nonlinear rank-order-based filtering of color images is difficult to implement; the multivariate nature of colors does not allow the introduction of a mathematically-correct and topology-preserving ordering relation. The most widely investigated approach is based on the use of reduced ordering relations introduced according to different scalars. We propose pseudo-morphologic and median operators based on reduced ordering of colors, with respect to scalars computed as geometrical shape invariants of a triangle representation of colors. The same color representation allows the introduction of a luminance invariant intercolor distance, used with good results in distance-based color filters.

In this paper, we propose a segmentation scheme for magnetic resonance (MR) images based on a two step algorithm. The first step consists of a classification based on an evidential k-NN rule initially proposed by Denoeux (1995). The second step allows to take into account the spatial dependence of each voxel of the MR volume in order to lead the segmentation. The goal is to locate properly tumors in MR images of the brain allowing the 3D reconstruction of the different brain structures and the tumor. It can help clinicians observe the tumors accurately and to follow the evolution of the tumors in multidate acquisitions of MR images.

Color edge detection has been normally based on the vector extension of classical (scalar) derivative operators. This extension has been done either by the independent processing of each color component and aggregation of the partial results or by the synthesis of a special color space, featuring a single highly relevant component. These approaches fail to embed any visual perception information. This paper proposes the use of a perceptually relevant dissimilarity measure, based on a fuzzy color model and on a spatial symmetry color spread index as the basis of a color edge detector.

This paper presents a multiple resolution algorithm for the segmentation of three-dimensional magnetic resonance (MR) images. The algorithm consists in the unsupervised segmentation of the MR volume into regions of different statistical behavior. Firstly, an unsupervised merging algorithm estimates a block segmentation of the volume while determining the region number and the parameters of those regions. This estimation is computed by minimizing a global information criterion. Next, the small regions are eliminated using statistic criteria. Finally, the segmentation is performed using the neighboring relationships between voxels via hidden Markov random fields and a multiple resolution iterated conditional mode algorithm. Some results on volumetric brain MR images are presented and discussed.

We propose a simple and new way of defining the directional wavelet packets basis. This new decomposition is based on a discrete rotation. To avoid information loss or modification (in order to keep the orthogonality property) we use a new one-to-one discrete rotation. This rotation is based on three discrete shear transformations. This new oriented basis does not divide the 2D Fourier plane into square regions. Instead of horizontal and vertical favourite directions, our directional scheme treats different arbitrary directions.

We study the problem of estimating the log-spectrum of a stationary Gaussian time series by thresholding the wavelet coefficients. We propose the use of the undecimated wavelet transform to denoise the log-periodogram. For this, we review a denoising method based on undecimated wavelet transform, and we propose a level-dependent threshold which considers that one undecimated scale has N/b coefficients "repeating" b times. The result corresponds to the average of all log-peridogram circulant shifts denoised by a decimated wavelet transform. The purpose of this undecimated thresholding is to make the reconstructed log-spectrum as nearly noise-free as possible, but with a keep of all small frequential components. Since the wavelet denoising method can be generalized to images, we develop an estimation technique of the 2D log-spectrum based on 2D undecimated wavelet. We derive a new technique, easy to apply, which gives information about the 2D frequential components of an image.

In this article, we propose a simple algorithm allowing the research of stationary partitions in locally stationary 2D processes, by use of adapted local bases like the local 2D DCT. The algorithm aims at finding some windows for which the width is adapted to the rate of change in the 2D spectrum. For this, we define an anisotropic Malvar's decomposition with a weak complexity and we propose a robust estimation of the difference in spectra, based on a denoising of the 2D log-periodogram with the help of the undecimated wavelet transform. Then, we consider the "symmetrical case" in the best partition selection method and a post-treatment that permits us to deal with the 2D nonuniform partitions is introduced. Our algorithm obtains better results than the classical Malvar's decomposition. It must be considered as a first treatment, which selects a global segmentation.