David Helbert

3-D Discrete Analytical Ridgelet Transform

In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient

Photometric reconstruction of a dynamic textured surface from just one color image acquisition

Textured surface analysis is essential for many applications. We present a three-dimensional recovery approach for real textured surfaces based on photometric stereo. The aim is to be able to measure the textured surfaces with a high degree of accuracy. For this, we use a color digital sensor and principles of color photometric stereo. This method uses a single color image, instead of a sequence of gray-scale images, to recover the surface of the three dimensions. It can thus be integrated into dynamic systems where there is significant relative motion between the object and the camera. To evaluate the performance of our method, we compare it on real textured surfaces to traditional photometric stereo using three images. We thus show that it is possible to have similar results with just one color image.

3D fast ridgelet transform

In this paper, we present a fast implementation of the 3D ridgelet transform based on discrete analytical 3D lines: the 3D discrete analytical ridgelet transform (DART). This transform uses the Fourier strategy (the projection-slice formula) for the computation of the associated discrete Radon transform. The innovative step of the DART is the construction of 3D discrete analytical lines in the Fourier domain, that allows a fast perfect backprojection. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a DART adapted to a specific application. A denoising application is presented.

Metric tensor for multicomponent edge detection

In this paper, we present the use of differential geometry for the segmentation of multispectral images, which allows us to unify several known methods including projecting onto a particular axis or a particular plan. This is done by choosing a metric tensor on the feature space computing the pullback of the metric tensor and applying standard Di Zenzo algorithm.

Ridgelet decomposition: discrete implementation and color denoising

In this paper, we review an implementation of the Ridgelet transform: The Discrete Analytical Ridgelet Transform (DART). This transform uses the Fourier strategy for the computation of the associated 2-D and 3-D discrete Radon transforms. The innovative step is the definition of a discrete 3-D transform and the construction of discrete analytical lines in the Fourier domain. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a DART adapted to a specific application. Indeed, the DART representation is not orthogonal, it is associated with a flexible redundancy factor. The DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. We had proved in different publications that the 2D and 3D DART are performant for the level of greys images restorations. Therefore we have interesting to 2D/3D color image restorations. We have compared the restoration results in function of different color space definition and importance of the white Gaussian noise. We criticize our results with two different measures : the Signal Noise Ratio calculation and perceptual measures to evaluate the perceptual colour difference between original and denoised images. These experimental results show that the simple thresholding of the DART coefficients is competitive than classical denoising techniques.

Color graph based wavelet transform with perceptual information

Abstract. We propose a numerical strategy to define a multiscale analysis for color and multicomponent images based on the representation of data on a graph. Our approach consists of computing the graph of an image using the psychovisual information and analyzing it by using the spectral graph wavelet transform. We suggest introducing color dimension into the computation of the weights of the graph and using the geodesic distance as a mean of distance measurement. We thus have defined a wavelet transform based on a graph with perceptual information by using the CIELab color distance. This new representation is illustrated with denoising and inpainting applications. Overall, by introducing psychovisual information in the graph computation for the graph wavelet transform, we obtain very promising results. Thus, results in image restoration highlight the interest of the appropriate use of color information.

Compressive template matching on multispectral data

This paper adapts a new template matching and target detection algorithm in multispectral images to a compressive sensing strategy. That template matching algorithm found in [1] relies on particular properties of L1 minimization algorithms to succeed. We propose a new algorithm that is reconstructing in a single step the location of a given signature of interest bypassing the image reconstruction and the template matching algorithm on that image. For that purpose, we use a modified split Bregman algorithm with various regularizers. We conduct numerical experiments on real-world multispectral image.

Rough Surfaces and Relief Extraction by Generalized Lambertian's Photometric Model

Within the framework of the analysis of 3D textured environment through image analysis, we approach here the case of the rough surfaces for the analysis of the local variations of their relief. Generally, the interaction between the light and these local relief variations leads to a textured image of these surfaces. The proposed approach is an original stereovision adaptation based on photometric model to the case of surfaces with a high degree of roughness and with Lamberts photometric behaviour. Indeed, the usual approach treats only the case of surfaces with weak roughness, without consideration of the phenomena such as interreflexions, shades or still maskings between elementary facets of surface. We propose to take into account these phenomena through the adaptation of Oren-Nayars model for the photometric stereovision. A comparative study is done to put out the contribution of the proposed approach in the case of rough surfaces.

Relief extraction of rough textured reflecting surface by image processing

Rough surface relief extraction is generally made by a mechanical method using a tactile sensor or by using an auto-focus laser sensor. With these sensors we can estimate surface relief from the analysis of a series of profiles. Since these measurements spend a lot of time, we hope that we can determine the relief by image processing. Several methods in the field of image processing have been proposed for relief extraction, such as shape from shading, optical flow, shape from focus and photometric stereovision. Our works are based on the photometric stereovision. In 1980, Woodham indicated that the relief of a Lambertian surface can be determined by the exploitation of a photometric model, which takes into account camera and light source positions according to the plan of surface. The proposed model expresses the gray level on the image according to the local relief variations. Three images of the same relief obtained under different angles of lighting are used to reconstruct the surface relief. From the method of Woodham, several important ameliorations have been proposed by other researchers. But a limit study in section 2.1.3 proves that the above methods worked with Lamberts model is adapted to the diffuse reflection, but not to the specular reflection. Thus, we propose another method to extract the relief of rough textured reflecting surface. In the proposed method, we show that the diffuse and specular components of the acquired images can be decomposed in two independent components. The diffuse component can be processed by Lamberts model, the specular component can be processed according to the position knowledge of facets. Finally, section 3 presents the experimental results obtained by this method, and compares measurement precision with the experimental results obtained by Lamberts model.

SPECTRAL GRAPH WAVELET BASED NONRIGID IMAGE REGISTRATION

We propose a nonrigid registration method whose motion estimation is cast into a feature matching problem under the Log-Demons framework using Graph Wavelets. We investigate the Spectral Graph Wavelets (SGWs) to capture the shape features of the images. The SGWs are more adapted to learn the spatial and geometric organization of data with complex structures than the classical wavelets. Our experiments on T1 brain images and endomicroscopic images show that this method outperforms the existing nonrigid image registration techniques (i.e. Log-Demons and Spectral Log-Demons) with improved similarity values.