Étienne Baudrier

A fast binary-image comparison method with local-dissimilarity quantification

Image similarity measure is widely used in image processing. For binary images that are not composed of a single shape, a local comparison is interesting but the features are usually poor (color) or difficult to extract (texture, forms). We present a new binary image comparison method that uses a windowed Hausdorff distance in a pixel-adaptive way. It enables to quantify the local dissimilarities and to give their spatial distribution which greatly improves the dissimilarity information. Combined with a support vector machine classifier, this method is successfully tested on a medieval-impression database

About Multigrid Convergence of Some Length Estimators

An interesting property for curve length digital estimators is the convergence toward the continuous length and the associate convergence speed when the digitization step h tends to 0. On the one hand, it has been proved that the local estimators do not verify this convergence. On the other hand, DSS and MLP based estimators have been proved to converge but only under some convexity and smoothness or polygonal assumptions. In this frame, a new estimator class, the so called semi-local estimators, has been introduced by Daurat et al. in [4]. For this class, the pattern size depends on the resolution but not on the digitized function. The semi-local estimator convergence has been proved for functions of class \(\mathcal{C}^2\) with an optimal convergence speed that is a \(\mathcal{O}(h^{\frac 1 2})\) without convexity assumption (here, optimal means with the best estimation parameter setting). A semi-local estimator subclass, that we call sparse estimators, is exhibited here. The sparse estimators are proved to have the same convergence speed as the semi-local estimators under the weaker assumptions. Besides, if the continuous function that is digitized is concave, the sparse estimators are proved to have an optimal convergence speed in h. Furthermore, assuming a sequence of functions \(G_h\colon h\mspace{1.0mu}\mathbb{Z} \to h\mspace{1.0mu}\mathbb{Z}\) discretizing a given Euclidean function as h tends to 0, sparse length estimation computational complexity in the optimal setting is a \(\mathcal{O}(h^{-\frac{1}{2}})\).

Curve Digitization Variability

This paper presents a study on the set of digitizations generated by the action of a group of transformations on a continuous curve before the digitization step. An upper bound for the cardinal of this digitization set under the translation group action is exhibited. Then this bound is tested on several functions. Finally, a representation of this digitization set is proposed and an illustration of its potential use is given on a length estimator.

A new similarity measure using Hausdorff distance map

Image dissimilarity measure is a hot topic. The measuring process is generally composed of an information mining in each image which results in an image signature and then a signature comparison to make the decision about the image similarity. In the scope of binary images, we propose to replace the information mining by a new straight image comparison which does not require a priori knowledge. The second stage is then replaced by a decision process based on the image comparison. The new comparison process is structured as follows: a morphological multiresolution analysis is applied to the two images. Secondly a distance map is constructed at each scale by the computation of the Hausdorff distance, restricted through a sliding-window. A signature is then extracted from the distance map and is used to make the decision. As an application, the algorithm has been successfully tested on an ancient illustration database.

Object digitization up to a translation

Abstract This paper presents a study on the set of the digitizations generated by all the translations of a planar body on a square grid. First the translation vector set is reduced to a bounded subset, then the dual introduced in [1] linking the translation vector to the corresponding digitization is proved to be piecewise constant. Finally, a new algorithm is proposed to compute the digitization set using the dual.

A new ab initio reconstruction method from unknown-direction projections of 2D binary set

This article focuses on the tomographic reconstruction of 2D binary images from projections whose directions are unknown. Observing that there is a mutual influence between the image reconstruction and the directions reconstruction, a new ab-initio method based on joint reconstruction of directions and image is proposed for 2D binary objects. Its implementation is done by optimizing a cost function taking as arguments the input projections, the current reconstructed image and the current directions. The optimization of the cost function is based on simulated annealing. After detailing the cost function, we test the proposed method for different resolutions and different noise levels. Finally, we present the future development of this promising method.

A new image quality measure considering perceptual information and local spatial feature

This paper presents a new comparative objective method for image quality evaluation. This method relies on two keys points: a local objective evaluation and a perceptual gathering. The local evaluation concerns the dissimilarities between the degraded image and the reference image; it is based on a gray-level local Hausdorff distance. This local Hausdorff distance uses a generalized distance transform which is studied here. The evaluation result is a local dissimilarity map (LDMap). In order to include perceptual information, a perceptual map based on the image properties is then proposed. The coefficients of this map are used to weight and to gather the LDMap measures into a single quality measure. The perceptual map is tunable and it gives encouraging quality measures even with naive parameters.

Study on the digitization dual combinatorics and convex case

The action of a translation on a continuous object before its digitization generates several digitizations. The dual, introduced by the authors in a previous paper, stands for these digitizations in function of the translation parameters. This paper focuses on the combinatorics of the dual by making a link between the digitization number and the boundary curve, especially through its dual representation. The convex case is then studied and a few significant examples are exhibited.

Joint 3D alignment-reconstruction multi-scale approach for cryo electron tomography

3D volume reconstruction in cryo-electron tomography is possible by using Transmission Electron Microscope (TEM) images from different tilt angles. The misalignment of these images is one of the limits to the quality of the reconstructed object. There are many alignment techniques to deal with this problem. Their common feature is to correct the 2D geometric transformation in the projection images. Nevertheless, 3D geometric transformation can occur in the TEM acquisition including tilt angular uncertainty. In this paper, we proposed a new multi-scale approach based on a Conjugate Gradient optimization of a cost function between the 3D reconstructed and the projection images with the purpose to find all the 3D parameters of geometric transformation. Tests on synthetic and real data prove the accuracy of our geometric transformation estimation.

Angular Uncertainty Refinement and Image Reconstruction Improvement in Cryo-electron Tomography

In the field of cryo-electron tomography (cryo-ET), numerous approaches have been proposed to tackle the difficulties of the three-dimensional reconstruction problem. And that, in order to cope with (1) t e missing and noisy data from the collected projections, (2) errors in projection images due to acquisition problems, (3) the capacity of processing large data sets and parameterizing the contrast function of the electron microscopy. In this paper, we present a novel approach for dealing with angular uncertainty in cryo-ET. To accomplish this task we propose a cost function and with the use of the nonlinear version of the optimization algorithm called Conjugate Gradient, we minimize it. We test the efficiency of our algorithm with both simulated and real data.