Julie Delon

Wasserstein barycenter and its application to texture mixing

This paper proposes a new definition of the averaging of discrete probability distributions as a barycenter over the Monge-Kantorovich optimal transport space. To overcome the time complexity involved by the numerical solving of such problem, the original Wasserstein metric is replaced by a sliced approximation over 1D distributions. This enables us to introduce a new fast gradient descent algorithm to compute Wasserstein barycenters of point clouds. This new notion of barycenter of probabilities is likely to find applications in computer vision where one wants to average features defined as distributions. We show an application to texture synthesis and mixing, where a texture is characterized by the distribution of the response to a multi-scale oriented filter bank. This leads to a simple way to navigate over a convex domain of color textures.

SAR-SIFT: A SIFT-Like Algorithm for SAR Images

The scale-invariant feature transform (SIFT) algorithm and its many variants are widely used in computer vision and in remote sensing to match features between images or to localize and recognize objects. However, mostly because of speckle noise, it does not perform well on synthetic aperture radar (SAR) images. In this paper, we introduce a SIFT-like algorithm specifically dedicated to SAR imaging, which is named SAR-SIFT. The algorithm includes both the detection of keypoints and the computation of local descriptors. A new gradient definition, yielding an orientation and a magnitude that are robust to speckle noise, is first introduced. It is then used to adapt several steps of the SIFT algorithm to SAR images. We study the improvement brought by this new algorithm, as compared with existing approaches. We present an application of SAR-SIFT to the registration of SAR images in different configurations, particularly with different incidence angles.

A Nonparametric Approach for Histogram Segmentation

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

Shape-based Invariant Texture Indexing

This paper introduces a new texture analysis scheme, which is invariant to local geometric and radiometric changes. The proposed methodology relies on the topographic map of images, obtained from the connected components of level sets. This morphological tool, providing a multi-scale and contrast-invariant representation of images, is shown to be well suited to texture analysis. We first make use of invariant moments to extract geometrical information from the topographic map. This yields features that are invariant to local similarities or local affine transformations. These features are invariant to any local contrast change. We then relax this invariance by computing additional features that are invariant to local affine contrast changes and investigate the resulting analysis scheme by performing classification and retrieval experiments on three texture databases. The obtained experimental results outperform the current state of the art in locally invariant texture analysis.

Midway Image Equalization

Midway image equalization means any method giving to a pair of images the same histogram, while maintaining as much as possible their previous grey level dynamics. In this paper, we present an axiomatic analysis of image equalization which leads us to derive two possible methods. Both methods are then compared in theory and in practice for two reliability criteria, namely their effect on quantization noise and on the support of the Fourier spectrum. A mathematical analysis of the properties of the methods is performed. Their algorithms are described and they are tested on such typical pairs as satellite image stereo pairs and different photographs of a same painting.

Accurate Junction Detection and Characterization in Natural Images

Accurate junction detection and characterization are of primary importance for several aspects of scene analysis, including depth recovery and motion analysis. In this work, we introduce a generic junction analysis scheme. The first asset of the proposed procedure is an automatic criterion for the detection of junctions, permitting to deal with textured parts in which no detection is expected. Second, the method yields a characterization of L-, Y- and X- junctions, including a precise computation of their type, localization and scale. Contrary to classical approaches, scale characterization does not rely on the linear scale-space. First, an a contrario approach is used to compute the meaningfulness of a junction. This approach relies on a statistical modeling of suitably normalized gray level gradients. Then, exclusion principles between junctions permit their precise characterization. We give implementation details for this procedure and evaluate its efficiency through various experiments.

A Statistical Approach to the Matching of Local Features

This paper focuses on the matching of local features between images. Given a set of query descriptors and a database of candidate descriptors, the goal is to decide which ones should be matched. This is a crucial issue, since the matching procedure is often a preliminary step for object detection or image matching. In practice, this matching step is often reduced to a specific threshold on the Euclidean distance to the nearest neighbor. Our first contribution is a robust distance between descriptors, relying on the adaptation of the Earth Movers Distance to circular histograms. It is shown that this distance outperforms classical distances for comparing SIFT-like descriptors, while its time complexity remains reasonable. Our second and main contribution is a statistical framework for the matching procedure, which yields validation thresholds automatically adapted to the complexity of each query descriptor and to the diversity and size of the database. The method makes it possible to detect multiple occurrences, as well as to deal with situations where the target is not present. Its performances are tested through various experiments on a large image database.

Small Baseline Stereovision

Abstract This paper presents a study of small baseline stereovision. It is generally admitted that because of the finite resolution of images, getting a good precision in depth from stereovision demands a large angle between the views. In this paper, we show that under simple and feasible hypotheses, small baseline stereovision can be rehabilitated and even favoured. The main hypothesis is that the images should be band limited, in order to achieve sub-pixel precisions in the matching process. This assumption is not satisfied for common stereo pairs. Yet, this becomes realistic for recent spatial or aerian acquisition devices. In this context, block-matching methods, which had become somewhat obsolete for large baseline stereovision, regain their relevance. A multi-scale algorithm dedicated to small baseline stereovision is described along with experiments on small angle stereo pairs at the end of the paper.

A Unified Framework for Detecting Groups and Application to Shape Recognition

A unified a contrario detection method is proposed to solve three classical problems in clustering analysis. The first one is to evaluate the validity of a cluster candidate. The second problem is that meaningful clusters can contain or be contained in other meaningful clusters. A rule is needed to define locally optimal clusters by inclusion. The third problem is the definition of a correct merging rule between meaningful clusters, permitting to decide whether they should stay separate or unite. The motivation of this theory is shape recognition. Matching algorithms usually compute correspondences between more or less local features (called shape elements) between images to be compared. Each pair of matching shape elements leads to a unique transformation (similarity or affine map.) The present theory is used to group these shape elements into shapes by detecting clusters in the transformation space.

Circular Earth Mover’s Distance for the comparison of local features

Many computer vision algorithms make use of local features, and rely on a systematic comparison of these features. The chosen dissimilarity measure is of crucial importance for the overall performances of these algorithms and has to be both robust and computationally efficient. Some of the most popular local features (like SIFT [4] descriptors) are based on one-dimensional circular histograms. In this contribution, we present an adaptation of the Earth moverpsilas distance to one-dimensional circular histograms. This distance, that we call CEMD, is used to compare SIFT-like descriptors. Experiments over a large database of 3 million descriptors show that CEMD outperforms classical bin-to-bin distances, while having reasonable time complexity.