Displacement Following of Hidden Objects in a Video Sequence

In a video sequence, computing the motion of an object requires the continuity of the apparent velocity field. This property does not hold when the object is hidden by an occlusion during its motion. The minimization of an energy functional leads to a simple algorithm which allows the recovery of the most likely trajectory of the occluded object from optical flow data at the border of the occlusion. Optical flow used for developing our method is an improvement on any variational technique of computing it. This improvement is based on a multichannel segmentation.     

The Use of Size Functions for Comparison of Shapes Through Differential Invariants

For comparison of shapes under subgroups of the projective group, we can use a lot of invariants and especially differential invariants coming from multiscale analysis. But such invariants, as we have to compute curvature, are very sensitive to the noise induced by the dicretization grid. In order to resolve this problem we use size functions which can recognize the qualitative similarity between graphs of functions that should be theorically coinciding but, unfortunately, change their values due to the presence of noise. Moreover, we focus this study on a projective differential invariant which allows to decide if one shape can be considered as the deformation of another one by a rotation of the camera.     

Self-assembled boron nanowire Y-junctions

In this work, we demonstrate that boron nanowire Y-junctions can be synthesized in a self-assembled manner by fusing two individual boron nanowires grown inclined toward each other. We show that the presence of a second liquid, in addition to the liquid Au catalyst, is critical to the inclination of the boron nanowire. The structure of the BNYJ arrays that we report here may allow construction of three- or multiple-terminal nanowire devices directly on Si-based readout circuits through controlled nanowire growth.     

Projective analysis of 2-D images

The use of the heatlike equation has been extended to the projective case in order to find a projective analysis of curves and images; unfortunately, this formulation leads to a fifth-order partial differential equation (PDE) that is not easy to implement. Thanks to the use of a three-dimensional (3-D) homogeneous representation of a picture, we present an alternative. Roughly speaking, it is a kind of decomposition of the heatlike formulation with well-posed second-order PDEs. The number of parameters goes from one to three (the scale parameter and two direction parameters). Moreover, this study allows us to propose a simplified multiscale analysis, which is given by an unique PDE (one parameter), for the subgroup of the projective transformations associated, up to a nonzero scalar factor, to an orthogonal 3x3 matrix.     

An Optimal Weight Method for CT Image Denoising

This paper proposes a novel exemplar- based method for reducing noise in computed tomography （CT） images. In the proposed method, denoising is performed on each block with the help of a given database of standard image blocks. For each noisy block, its denoised version is the best sparse positive linear combination of the blocks in the database. We formulate the problem as a constrained optimization problem such that the solution is the denoised block. Experimental results demonstrate the good performance of the proposed method over current state-of-the-art denoising methods, in terms of both objective and subjective evaluations.     

Camera Motion Estimation Through Planar Deformation Determination

In this paper, we propose a global method for estimating the motion of a camera which films a static scene. Our approach is direct, fast and robust, and deals with adjacent frames of a sequence. It is based on a quadratic approximation of the deformation between two images, in the case of a scene with constant depth in the camera coordinate system. This condition is very restrictive but we show that, provided translation and depth inverse variations are small enough, the error on optical flow involved by the approximation of depths by a constant is small. In this context, we propose a new model of camera motion which allows to separate the image deformation in a similarity and a “purely” projective application, due to change of optical axis direction. This model leads to a quadratic approximation of image deformation that we estimate with an M-estimator; we can immediately deduce camera motion parameters. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.