Exemplar-based methods have proven their efficiency for the reconstruction of missing parts in a digital image. Texture as well as local geometry are often very well restored by such methods. Some applications, however, require the ability to reconstruct nonlocal geometric features, e.g., long edges. In order to do so, we propose to first compute a geometric sketch, which is then interpolated and used as a guide for the global reconstruction. In comparison with other related approaches, the originality of our work relies on the following points: (1) The geometric sketch computation is parameter-free and based on level lines, which provides a complete, reliable, and stable representation of the image. (2) The completion of the geometric sketch is fully automatic. It is done using a new—and interesting on its own—geometric inpainting approach that interpolates level lines with Euler spirals. Euler spirals are natural curves for shape completion and have been used already for edge completion and inpainting. It is the first time, however, that these curves are used for completing the whole level lines structure. (3) The general reconstruction is performed using a guided version of a classical exemplar-based method. However, we do not constrain the exemplar-based reconstruction to strictly follow the geometric guide. We actually use a new metric between blocks that consists of the sum of the classical ${{\mathrm L}^2}$ metric between any two blocks of the general image plus an ${{\mathrm L}^2}$ metric between the corresponding blocks in the completed geometric image. This is equivalent to a Lagrangian relaxation of a strictly guided reconstruction. We discuss in the paper the details of the method and some related mathematical issues, and we illustrate its efficiency on several examples.

This paper introduces a variational formulation for image denoising based on a quadratic function over kernels of variable bandwidth. These kernels are scale adaptive and reflect spatial and photometric similarities between pixels. The bandwidth of the kernels is observation-dependent towards improving the accuracy of the reconstruction process and is constrained to be locally smooth. We analyze the evolution of the noise model form the RAW space to the RGB one, by propagating it over the image formation process. The experimental results demonstrate that the use of a variable bandwidth approach and an image intensity dependent noise variance ensures better restoration quality.

This paper presents a method for detecting independent temporally-persistent motion patterns in image sequences. The result is a description of the dynamic content of a video sequence in terms of moving objects, their number, image position and approximate motion. For each detected motion pattern a local trajectory as well as a confidence level is provided. The method is based on local motion measurements extracted from short video segments. These measurements are mapped in an adequate grouping space where independent trajectories correspond to distinct clusters. The automatic cluster detection is handled in an a contrario framework, which is general and involves no parameter tuning. The method was validated on real video sequences featuring rigid and non-rigid moving objects, static and mobile cameras, and distracting motions. The output of this method could initialize tracking algorithms. Applications of interest are robot navigation, car-driver assistance, surveillance and activity recognition.

Psychovision have shown that many grouping laws come into play to structure human vision. They use informations of different kinds, not only gray (or color)-level values. Here we will show how an orientation interpolation operator working in S1(angle in [0, 2π]) can be used to recover geometrical information in images. The operator is presented and is used to produce fields that drive a fast marching contour extraction algorithm and a LIC-based smoothing method. Experiment on real images are reported to validate the proposed approach.

This paper copes with the reconstruction of accretionary morphogenesis within a given observation plane from an image depicting successive (typically seasonal or daily) growth structures. Modeling accretionary growth shapes as the level-sets of a potential function, a variational framework is derived from geometric criteria. It resorts to minimizing an energy functional involving two terms: a regularization term and a data-driven term which constrain the evolution of the shapes with respect to a growth orientation field. Experiments carried out on real data (e.g., fish otoliths) validate the proposed approach, which opens new research directions for information extraction and decoding from biological archives.

A contrario modeling is a detection framework based on a perceptual grouping principle. Based on an existing a contrario motion detection method, this paper presents two solutions for improving detection results by using the confidence levels issued from the a contrario testing framework. The first one embeds the confidence levels in a maximality principle in order to operate a sensible selection among detections. This improves the description of the moving objects. The second extension enables to take into account information coming from more than one residual motion map in order to improve detection results on small slowly moving objects.

We propose a probabilistic algorithm able to detect the curves that are unexpectedly smooth in a set of digital curves. The only parameter is a false alarm rate, influencing the detection only by its logarithm. We experiment the good continuation criterion on image level lines. One of the conclusion is that, accordingly to Gestalt theory, one can detect edges in a way that is widely independent of contrast. We also use the same kind of method to detect corners and junctions.

Shape recognition systems usually order a fixed number of best matches to each query, but do not address or answer the two following questions: Is a query shape in a given database? How can we be sure that a match is correct? This communication deals with these two key points. A database being given, with each shape S and each distance /spl delta/, we associate its number of false alarms NFA(S, /spl delta/), namely the expectation of the number of shapes at distance /spl delta/ in the database. Assume that NFA(S, /spl delta/) is very small with respect to 1, and that a shape S' is found at distance /spl delta/ from S in the database. This match could not occur just by chance and is therefore a meaningful detection. Its explanation is usually the common origin of both shapes. Experimental evidence will show that NFA(S, /spl delta/) can be predicted accurately.

Interpolation of digital elevation models becomes necessary in many situations, for instance, when constructing them from contour lines (available e.g., from nondigital cartography), or from disparity maps based on pairs of stereoscopic views, which often leaves large areas where point correspondences cannot be found reliably. The absolutely minimizing Lipschitz extension (AMLE) model is singled out as the simplest interpolation method satisfying a set of natural requirements. In particular, a maximum principle is proven, which guarantees not to introduce unnatural oscillations which is a major problem with many classical methods. The authors then discuss the links between the AMLE and other existing methods. In particular, they show its relation with geodesic distance transformation. They also relate the AMLE to the thin-plate method, that can be obtained by a prolongation of the axiomatic arguments leading to the AMLE, and addresses the major disadvantage of the AMLE model, namely its inability to interpolate slopes as it does for values. Nevertheless, in order to interpolate slopes, they have to give up the maximum principle and authorize the appearance of oscillations. They also discuss the possible link between the AMLE and Kriging methods that are the most widely used in the geoscience literature.