A numerical realistic 3D anthropomorphic breast model is useful for evaluating breast imaging applications. A method is proposed to model small and medium-scale fibroglandular and intra-glandular adipose tissues observed in the center part of clinical breast CT images. The method builds upon a previously proposed model formulated as stochastic geometric processes with mathematically tractable parameters. In this work, the medium-scale parameters were automatically and objectively inferred from breast CT images. We hypothesized that a set of random ellipsoids exhibiting cluster interaction is representative to model the medium-scale intra-glandular adipose compartments. The ellipsoids were reconstructed using a multiple birth, death and shift algorithm. Then, a Matérn cluster process was used to fit the reconstructed ellipsoid centers. Finally, distributions of the ellipsoid shapes and orientations were estimated using maximum likelihood estimators. Feasibility was demonstrated on 16 volumes of interests (VOI). To assess the realism of the 3D breast texture model, β and LFE metrics computed in simulated projection images of simulated texture realizations and clinical images were compared. Visual realism was illustrated. For 12 out of 16 VOIs, our hypothesis on clustering interaction process is confirmed. The average β values from simulated texture images (3.7 to 4.2) of the 12 different VOIs are higher than the average β value from 2D clinical images (2.87). LFE of simulated texture images and clinical mammograms are similar. Compared to our previous model, whereby simulation parameters were based upon empirical observations, our inference method substantially augments the ability to generate textures with higher visual realism and larger morphological variety.

Many generative models synthesize data by transforming a standard Gaussian random variable using a deterministic neural network. Among these models are the Variational Autoencoders and the Generative Adversarial Networks. In this work, we call them "push-forward" models and study their expressivity. We formally demonstrate that the Lipschitz constant of these generative networks has to be large in order to fit multimodal distributions. More precisely, we show that the total variation distance and the Kullback-Leibler divergence between the generated and the data distribution are bounded from below by a constant depending on the mode separation and the Lipschitz constant. Since constraining the Lipschitz constants of neural networks is a common way to stabilize generative models, there is a provable trade-off between the ability of push-forward models to approximate multimodal distributions and the stability of their training. We validate our findings on one-dimensional and image datasets and empirically show that the recently introduced diffusion models do not suffer of such limitation.

Determinantal point processes (DPPs) are probabilistic models of configurations that favor diversity or repulsion. They have recently gained influence in the machine learning community, mainly because of their ability to elegantly and efficiently subsample large sets of data. In this paper, we consider DPPs from an image processing perspective, meaning that the data we want to subsample are pixels or patches of a given image. To this end, our framework is discrete and finite. First, we adapt their basic definition and properties to DPPs defined on the pixels of an image, that we call determinantal pixel processes (DPixPs). We are mainly interested in the repulsion properties of such a process and we apply DPixPs to texture synthesis using shot noise models. Finally, we study DPPs on the set of patches of an image. Because of their repulsive property, DPPs provide a strong tool to subsample discrete distributions such as that of image patches.

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.

We consider the problem of detecting small targets in videos where the textured background is also possibly moving. The proposed method is based on a two steps statistical framework. In a first step, the optical flow is computed using a pyramidal scheme incorporating statistical tests for a result with reliability guarantees. In the second step, the detection of targets is changed into a problem of anomaly detection in noise, and statistical testing ensures a control of the number of false detections.

In this work we introduce a statistical framework in order to analyze the spatial redundancy in natural images. This notion of spatial redundancy must be defined locally. To do so, we define an auto-similarity function which, given one image, computes a dissimilarity measurement between patches. To derive a criterion for taking a decision on the similarity between two patches, we present an a contrario model. Namely, two patches are said to be similar if the associated dissimilarity measurement is unlikely to happen in a background model. Choosing Gaussian random fields as background models, we derive nonasymptotic expressions for the probability distribution function of similarity measurements. We present an algorithm in order to assess redundancy in natural images and discuss applications in denoising, periodicity analysis, and texture ranking.

Extraction of local features constitutes a first step of many algorithms used in computer vision. The choice of keypoints and local features is often driven by the optimization of a performance criterion on a given computer vision task, which sometimes makes the extracted content difficult to apprehend. In this paper we propose to examine the content of local image descriptors from a reconstruction perspective. For that, relying on the keypoints and descriptors provided by the scale-invariant feature transform (SIFT), we propose two stochastic models for exploring the set of images that can be obtained from given SIFT descriptors. The two models are both defined as solutions of generalized Poisson problems that combine gradient information at different scales. The first model consists in sampling an orientation field according to a maximum entropy distribution constrained by local histograms of gradient orientations (at scale 0). The second model consists in simple resampling of the local histogram of gradient orientations at multiple scales. We show that both of these models admit convolutive expressions which allow us to compute the model statistics (e.g., the mean, the variance). Also, in the experimental section, we show that these models are able to recover many image structures, while not requiring any external database. Finally, we compare several other choices of points of interest in terms of quality of reconstruction, which confirms the optimality of the SIFT keypoints over simpler alternatives.

The main approaches to texture modeling are the statistical psychophysically inspired model and the patch-based model. In the first model the texture is characterized by a sophisticated statistical signature. The associated sampling algorithm estimates this signature from the example and produces a genuinely different texture. This texture nevertheless often loses accuracy. The second model boils down to a clever copy-paste procedure, which stitches verbatim copies of large regions of the example. We propose in this communication to involve a locally Gaussian texture model in the patch space. It permits to synthesize textures that are everywhere different from the original but with better quality than the purely statistical methods.

In this paper, we address the problem of the restoration of images which have been affected by impulse noise or by a mixture of Gaussian and impulse noise. We rely on a patch-based approach, which requires careful choices for both the distance between patches and for the statistical estimator of the original patch. Experiments are run in the case of pure impulse noise and in the case of a mixture. The method proves to be particularly powerful, especially for the restoration of textured regions, and compares favorably to recent restoration methods.

In this paper, we show that a patch-based approach can successfully be applied for impulse noise removal. This requires careful choices for both the distance between patches and for the statistical estimator of the original patch. This method proves to be particularly powerful, especially for the restoration of textured areas, and compares favorably to recent restoration methods.

In this paper, we are interested in the mathematical analysis of the micro-textures that have the property to be perceptually invariant under the randomization of the phases of their Fourier Transform. We propose a compact representation of these textures by considering a special instance of them: the one that has identically null phases, and we call it “texton”. We show that this texton has many interesting properties, and in particular it is concentrated around the spatial origin. It appears to be a simple and useful tool for texture analysis and texture synthesis, and its definition can be extended to the case of color micro-textures.

In this paper, we address a complex image registration issue arising while the dependencies between intensities of images to be registered are not spatially homogeneous. Such a situation is frequently encountered in medical imaging when a pathology present in one of the images modifies locally intensity dependencies observed on normal tissues. Usual image registration models, which are based on a single global intensity similarity criterion, fail to register such images, as they are blind to local deviations of intensity dependencies. Such a limitation is also encountered in contrast-enhanced images where there exist multiple pixel classes having different properties of contrast agent absorption. In this paper, we propose a new model in which the similarity criterion is adapted locally to images by classification of image intensity dependencies. Defined in a Bayesian framework, the similarity criterion is a mixture of probability distributions describing dependencies on two classes. The model also includes a class map which locates pixels of the two classes and weighs the two mixture components. The registration problem is formulated both as an energy minimization problem and as a maximum a posteriori estimation problem. It is solved using a gradient descent algorithm. In the problem formulation and resolution, the image deformation and the class map are estimated simultaneously, leading to an original combination of registration and classification that we call image classifying registration. Whenever sufficient information about class location is available in applications, the registration can also be performed on its own by fixing a given class map. Finally, we illustrate the interest of our model on two real applications from medical imaging: template-based segmentation of contrast-enhanced images and lesion detection in mammograms. We also conduct an evaluation of our model on simulated medical data and show its ability to take into account spatial variations of intensity dependencies while keeping a good registration accuracy.

In this paper, we address the problem of the restoration of image sequences which have been affected by local intensity modifications (local contrast changes). Such artifacts can be encountered particularly in biological or archive film sequences, and are usually due to inconsistent exposures or sparse time sampling. In order to reduce such local artifacts, we introduce a local stabilization operator, called LStab, which acts as a time filter on image patches and relies on a similarity measure which is robust to contrast changes. Thereby, this operator is able to take motion into account without relying on a sophisticated motion estimation procedure. The efficiency of the stabilization is shown on various sequences. The experimental results compare favorably with state-of-the-art approaches.

In this work, we propose a method to segment a 1-D histogram without a priori assumptions about the underlying density function. Our approach considers a rigorous definition of an admissible segmentation, avoiding over and under segmentation problems. A fast algorithm leading to such a segmentation is proposed. The approach is tested both with synthetic and real data. An application to the segmentation of written documents is also presented. We shall see that this application requires the detection of very small histogram modes, which can be accurately detected with the proposed method.

Color palettes are an important tool for color image analysis, since they are the initial point of different techniques such as quantization or indexing. This paper presents a new method for the automatic construction of a color palette, which adjusts dynamically its number of colors according to the visual content of the image. The method is based on appropriately segmenting the HSI color space, which is achieved by individually partitioning the histograms associated to each color component. As a result we obtain a hierarchical color palette, which represents the color image with a reduced number of colors.

Even though vanishing points in digital images result from parallel lines in the 3D scene, most of the proposed detection algorithms are forced to rely heavily either on additional properties (like orthogonality or coplanarity and equal distance) of the underlying 3D lines, or on knowledge of the camera calibration parameters, in order to avoid spurious responses. In this work, we develop a new detection algorithm that relies on the Helmoltz principle recently proposed for computer vision by Desolneux et al (2001; 2003), both at the line detection and line grouping stages. This leads to a vanishing point detector with a low false alarms rate and a high precision level, which does not rely on any a priori information on the image or calibration parameters, and does not require any parameter tuning.

Wertheimer's theory suggests a general perception law according to which objects having a quality in common get perceptually grouped. The Helmholtz principle is a quantitative version of this general grouping law. It states that a grouping is perceptually "meaningful" if its number of occurrences would be very small in a random situation: geometric structures are then characterized as large deviations from randomness. In two previous works, we have applied this principle to the detection of orientation alignments and boundaries in a digital image. In this paper, we show that the method is fully general and can be extended to a grouping by any quality. We treat as an illustration the alignments of objects, their grouping by color and by size, and the vicinity gestalt (clusters). Collaboration of the gestalt grouping laws and their pyramidal structure are illustrated in a case study.

We address the problem of computing a local orientation map in a digital image. We show that standard image gray level quantization causes a strong bias in the repartition of orientations, hindering any accurate geometric analysis of the image. In continuation, a simple dequantization algorithm is proposed, which maintains all of the image information and transforms the quantization noise in a nearby Gaussian white noise (we actually prove that only Gaussian noise can maintain isotropy of orientations). Mathematical arguments are used to show that this results in the restoration of a high quality image isotropy. In contrast with other classical methods, it turns out that this property can be obtained without smoothing the image or increasing the signal-to-noise ratio (SNR). As an application, it is shown in the experimental section that, thanks to this dequantization of orientations, such geometric algorithms as the detection of nonlocal alignments can be performed efficiently. We also point out similar improvements of orientation quality when our dequantization method is applied to aliased images.