Stéphane Derrode

Robust and Efficient Fourier-Mellin Transform Approximations for Gray-Level Image Reconstruction and Complete Invariant Description

This paper addresses the gray-level image representation ability of the Fourier?Mellin transform (FMT) for pattern recognition, reconstruction, and image database retrieval. The main practical difficulty of the FMT lies in the accuracy and efficiency of its numerical approximation and we propose three estimations of its analytical extension. A comparison of these approximations is performed from discrete and finite-extent sets of Fourier?Mellin harmonics by means of experiments in: (i) image reconstruction via both visual inspection and the computation of a reconstruction error; and (ii) pattern recognition and discrimination by using a complete and convergent set of features invariant under planar similarities.Experimental results on real gray-level images show that it is possible to recover an image to within a specified degree of accuracy and to classify objects reliably even when a large set of descriptors is used. Finally, an example will be given, which illustrates both theoretical and numerical results in the context of content-based image retrieval.

Unsupervised change detection on SAR images using fuzzy hidden Markov chains

This work deals with unsupervised change detection in temporal sets of synthetic aperture radar (SAR) images. We focus on one of the most widely used change detector in the SAR context, the so-called log-ratio. In order to deal with the classification issue, we propose to use a new fuzzy version of hidden Markov chains (HMCs), and thus to address fuzzy change detection with a statistical approach. The main characteristic of the proposed model is to simultaneously use Dirac and Lebesgue measures at the class chain level. This allows the coexistence of hard pixels (obtained with the classical HMC segmentation) and fuzzy pixels (obtained with the fuzzy measure) in the same image. The quality assessment of the proposed method is achieved with several bidate sets of simulated images, and comparisons with classical HMC are also provided. Experimental results on real European Remote Sensing 2 Precision Image (ERS-2 PRI) images confirm the effectiveness of the proposed approach.

Signal and image segmentation using pairwise Markov chains

The aim of this paper is to apply the recent pairwise Markov chain model, which generalizes the hidden Markov chain one, to the unsupervised restoration of hidden data. The main novelty is an original parameter estimation method that is valid in a general setting, where the form of the possibly correlated noise is not known. Several experimental results are presented in both Gaussian and generalized mixture contexts. They show the advantages of the pairwise Markov chain model with respect to the classical hidden Markov chain one for supervised and unsupervised restorations.

Shape analysis and symmetry detection in gray-level objects using the analytical Fourier-Mellin representation

The analytical Fourier-Mellin transform is used in order to assess motion parameters between gray-level objects having the same shape with distinct scale and orientation. From results on commutative harmonic analysis, a functional is constructed in which the location of the minimum gives an estimation of the size and orientation parameters. Furthermore, when the set of geometrical transformations is restricted to the compact rotation group, we show that this minimum is exactly the Hausdorff distance between shapes represented in the Fourier-Mellin domain. This result is used for the detection and the estimation of both all rotation and reflection symmetries in objects.

Image reconstruction from a complete set of similarity invariants extracted from complex moments

Various types of moments have been used to recognize image patterns in a number of applications. However, only few works have paid attention to the completeness property of the invariant descriptor set, which is of fundamental importance from the theoretical as well as the practical points of views. This paper proposes a systematic method to extract a complete set of similarity invariants (translation, rotation and scale), by means of some linear combinations of complex moments. The problem of image reconstruction from a finite set of its moment invariants is then examined by exploiting the link between the discrete Fourier transform of an image and its complex moments. Experimental results are presented that confirm theoretical properties as well as numerical effectiveness of the method.

Unsupervised multiscale oil slick segmentation from SAR images using a vector HMC model

This study focuses on the segmentation and characterization of oil slicks on the sea surface from synthetic aperture radar (SAR) observations. In fact, an increase in viscosity due to oil notably reduces the roughness of the sea surface which plays a major part in the electromagnetic backscattering. So, an oil spill is characterized by low-backscattered energy and appears as a dark patch in a SAR image. This is the reason why most detection algorithms are based on histogram thresholding, but they do not appear to be satisfactory since the number of false alarms is generally high. By considering that a film has a specific impact on the ocean wave spectrum and by taking into account the specificity of SAR images, a vector hidden Markov chain (HMC) model adapted to a multiscale description of the original image is developed. It yields an unsupervised segmentation method that takes into account the different states of the sea surface through its wave spectrum. Thanks to mixture estimation, it is possible to characterize the detected areas and thus avoid most false alarms. Results of segmentation are shown in two types of scenarios. The first one concerns an oil spill in the Mediterranean sea detected by the ERS SAR sensor at a resolution of 25m. The second scenario is related to the wreck of the Prestige acquired by the Envisat ASAR sensor in a wide swath mode at a resolution of 150m.

Fourier-based geometric shape prior for snakes

A novel method of snakes with shape prior is presented in this paper. We propose to add a new force which makes the curve evolve to particular shape corresponding to a template to overcome some well-known problems of snakes. The template is an instance or a sketch of the researched contour without knowing its exact geometric pose in the image. The prior information is introduced through a set of complete and locally stable invariants to Euclidean transformations (translation, rotation and scale factor) computed using Fourier transform on contours. The method is evaluated with the segmentation of myocardial scintigraphy slices and the tracking of an object in a video sequence.

Invariant content-based image retrieval using a complete set of Fourier-Mellin descriptors

Image retrieval from a large database is an important and emerging search area. This retrieval requires the choice of a suitable set of image features, a method to extract them correctly, and a measure of the similarity between features that can be computed in real time. The paper presents a complete set of Fourier-Mellin descriptors for object storage and retrieval. Our approach is translation, rotation and scale invariant. Several retrieval examples in a large image database are presented.

Hyperspectral image segmentation with Markov chain model

The Hidden Markov Chain (HMC) model has been extended to take into consideration the multi-component representation of an hyperspectral data cube. Parameters estimation is performed using the general Iterative Conditional Estimation (ICE) method. The vectorial extension of the model is straightforward since the vectorial point of view joints the observation of each pixel as a spectral signature. Then, the segmentation procedure achieves an estimation of multi-dimensional correlated probability density functions (pdf). Multi-dimensional densities have been estimated by a set of 1D densities through a projection step that makes component independent and of reduced dimension. Classifications have been applied to an image from the CASI sensor including 17 bands (from 450 to 950 nm) representing an intensive agricultural region (Brittany, France). Since, the intrinsic dimensionality of the observation has been estimated to 4, the multi-component HMC model has been applied to the CASI image reduced to 4 bands through an adapted projection pursuit method.

Multiscale oil slick segmentation with Markov chain model

A Markov chain model is applied for the segmentation of oil slicks acquired by SAR sensors. Actually, oil slicks have specific impact on ocean wave spectra. Initial wave spectra may be characterized by three kinds of waves, big, medium and small, which correspond physically to gravity and gravity-capillary waves. The increase of viscosity due to the presence of oil damps gravity-capillary waves. This induces a damping of the backscattering to the sensor, but also a dampening of the energy of the wave spectra. Thus, local segmentation of wave spectra may be achieved by the segmentation of a multiscale decomposition of the original SAR image. In this work, the unsupervised segmentation is achieved by using a vectorial extension of the Hidden Markov Chain (HMC) model. Parameters estimation is performed using the general Iterative Conditional Estimation (ICE) method. The problem of estimating multi-dimensional and non-Gaussian densities is solved by using a Principal Component Analysis (PCA). The algorithm has been applied on an ERS-PRI image. It yields interesting segmentation results with a very limited number of false alarms. Also, the multiscale segmentation proved to be an interesting alternative to classify marginal or degraded slicks.