We describe a new fully unsupervised image segmentation method based on a Bayesian approach and a Potts-Markov random field (PMRF) model that are performed in the wavelet domain. A Bayesian segmentation model, based on a PMRF in the direct domain, has already been successfully developed and tested. This model performs a fully unsupervised segmentation, on images composed of homogeneous regions, by introducing a hidden Markov model (HMM) for the regions to be classified, and Gaussian distributions for the noise and for the pixels pertaining to each region. The computation of the posterior laws, deduced from these a priori distributions for the pixels, is done by a Markov chain Monte Carlo (MCMC) approach and uses a Gibbs sampling algorithm. The use of a high number of iterations to reach convergence in a segmentation, where the number of segments, or "classes" labels, is important, makes the algorithm rather slow for the processing of a large quantity of data like image sequences. To overcome this problem, we take advantage of the property of the wavelet coefficients, in an orthogonal decomposition, to be modeled by a mixture of two Gaussians. Thus, by projecting an observable noisy image in the wavelet domain, we are able to segment, in this same domain, the wavelet subbands in only two classes. After a decomposition up to a scale J, the main idea is to segment the coarse, and small, approximation subband with a high number of classes, and to segment all the detail (wavelet) subbands with only two classes. The segmented wavelet domain coefficients are then reconstructed to obtain a final segmented image in the direct domain. Our tests on synthetic and natural images show that the segmentation quality stays good, even with noisy images, and shows that the segmentation times can be significantly reduced.
We present here new results in Wavelet Multi-Resolution Analysis (W-MRA) applied to shape recognition in automatic vehicle driving applications. Different types of shapes have to be recognized in this framework. They pertain to most of the objects entering the sensors field of a car. These objects can be road signs, lane separation lines, moving or static obstacles, other automotive vehicles, or visual beacons. The recognition process must be invariant to global, affine or not, transformations which are : rotation, translation and scaling. It also has to be invariant to more local, elastic, deformations like the perspective (in particular with wide angle camera lenses), and also like deformations due to environmental conditions (weather : rain, mist, light reverberation) or optical and electrical signal noises. To demonstrate our method, an initial shape, with a known contour, is compared to the same contour altered by rotation, translation, scaling and perspective. The curvature computed for each contour point is used as a main criterion in the shape matching process. The original part of this work is to use wavelet descriptors, generated with a fast orthonormal W-MRA, rather than Fourier descriptors, in order to provide a multi-resolution description of the contour to be analyzed. In such way, the intrinsic spatial localization property of wavelet descriptors can be used and the recognition process can be speeded up. The most important part of this work is to demonstrate the potential performance of Wavelet-MRA in this application of shape recognition.