Multiresolution signal decomposition schemes

[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis and synthesis. This scheme comprises the following ingredients: (i) the pyramid consists of a (finite or infinite) number of levels such that the information content decreases towards higher levels; (ii) each step towards a higher level is constituted by an (information-reducing) analysis operator, whereas each step towards a lower level is modeled by an (information-preserving) synthesis operator. One basic assumption is necessary: synthesis followed by analysis yields the identity operator, meaning that no information is lost by these two consecutive steps. In this report, several examples are described of linear as well as nonlinear (e.g., morphological) pyramid decomposition schemes. Some of these examples are known from the literature (Laplacian pyramid, morphological granulometries, skeleton decomposition) and some of them are new (morphological Haar pyramid, median pyramid). Furthermore, the report makes a distinction between single-scale and multiscale decomposition schemes (i.e. without or with sample reduction).#[PNA-R9905] In its original form, the wavelet transform is a linear tool. However, it has been increasingly recognized that nonlinear extensions are possible. A major impulse to the development of nonlinea

Convergence of adaptive morphological filters in the context of Markov chains

A typical parameterized r-opening *r is a filter defined as a union of openings by a collection of compact, convex structuring elements, each of which is governed by a parameter vector r. It reduces to a single parameter r-opening filter by a set of structuring elements when r is a scalar sizing parameter. The parameter vector is adjusted by a set of adaptation rules according to whether the re construction Ar derived from r correctly or incorrectly passes the signal and noise grains sampled from the image. Applied to the signal-union-noise model, the optimization problem is to find the vector of r that minimizes the Mean-Absolute-Error between the filtered and ideal image processes. The adaptive r-opening filter fits into the framework of Markov processes, the adaptive parameter being the state of the process. For a single parameter r-opening filter, we proved that there exists a stationary distribution governing the parameter in the steady state and convergence is characterized in terms of the steady-state distribution. Key filter properties such as parameter mean, parameter variance, and expected error in the steady state are characterized via the stationary distribution. Steady-state behavior is compared to the optimal solution for the uniform model, for which it is possible to derive a closed-form solution for the optimal filter. We also developed the Markov adaptation system for multiparameter opening filters and provided numerical solutions to some special cases. For multiparameter r-opening filters, various adaptive models derived from various assumptions on the form of the filter have been studied. Although the state-probability increment equations can be derived from the appropriate Chapman-Kolmogorov equations, the closed-form representation of steady-state distributions is mathematically problematic due to the support geometry of the boundary states and their transitions. Therefore, numerical methods are employed to approximate for steady state probability distributions. The technique developed for conventional opening filters is also applied to bandpass opening filters. In present thesis study, the concept of signal and noise pass sets plays a central role throughout the adaptive filter analysis. The pass set reduces to the granulometric measure (or {&r}-measure) of the signal and noise grain. Optimization and adaptation are characterized in terms of the distribution of the granulometric measures for single parameter filters, or in terms of the multivariate distribution of the signal and noise pass sets. By introducing these concepts, this thesis study also provides some optimal opening filter error equations. It has been shown in the case of the uniform distribution of single sizing parameter that there is a strong agreement between the adaptive filter and optimal filter based on analytic error minimization. This agreement has been also demonstrated in various r-opening filters. Furthermore, the probabilistic interpretation has a close connection to traditional linear adaptive filter theory. The method has been applied to the classical grain separation (clutter removal) problem. *See content for correct numerical representation

Image sequence analysis and merging

Peer ReviewedPostprint (published version

One-Dimensional Openings, Granulometries and Component Trees in O(1) Per Pixel

International audienceWe introduce a new, efficient and adaptable algorithm to compute openings, granulometries and the component tree for one-dimensional (1-D) signals. The algorithm requires only one scan of the signal, runs in place in per pixel, and supports any scalar data precision (integer or floating-point data). The algorithm is applied to two-dimensional images along straight lines, in arbitrary orientations. Oriented size distributions can thus be efficiently computed, and textures characterized. Extensive benchmarks are reported. They show that the proposed algorithm allows computing 1-D openings faster than existing algorithms for data precisions higher than 8 bits, and remains competitive with respect to the algorithm proposed by Van Droogenbroeck when dealing with 8-bit images. When computing granulometries, the new algorithm runs faster than any other method of the state of the art. Moreover, it allows efficient computation of 1-D component trees

Texture Analysis with Arbitrarily Oriented Morphological Opening and Closing

13 pagesThis paper presents a fast, streaming algorithm for 1-D morphological opening on 2-D support. The algorithm is further extended to compute the complete size distribution during a single image run. The Structuring Element (SE) can be oriented under arbitrary angle that allows us to perform different orientation-involved image analysis, such as local angle extraction, directional granulometries, \etc The algorithm processes an image in constant time irrespective of the SE orientation and size, with a minimal latency and very low memory requirements. Regardless the SE orientation, it reads and writes data strictly sequentially in the horizontal scan order. Aforementioned properties allow an efficient implementation in embedded hardware platforms that opens a new opportunity of a parallel computation, and consequently, a significant speed-up

Detection of Neovascularization Based on Fractal and Texture Analysis with Interaction Effects in Diabetic Retinopathy

Diabetic retinopathy is a major cause of blindness. Proliferative diabetic retinopathy is a result of severe vascular complication and is visible as neovascularization of the retina. Automatic detection of such new vessels would be useful for the severity grading of diabetic retinopathy, and it is an important part of screening process to identify those who may require immediate treatment for their diabetic retinopathy. We proposed a novel new vessels detection method including statistical texture analysis (STA), high order spectrum analysis (HOS), fractal analysis (FA), and most importantly we have shown that by incorporating their associated interactions the accuracy of new vessels detection can be greatly improved. To assess its performance, the sensitivity, specificity and accuracy (AUC) are obtained. They are 96.3%, 99.1% and 98.5% (99.3%), respectively. It is found that the proposed method can improve the accuracy of new vessels detection significantly over previous methods. The algorithm can be automated and is valuable to detect relatively severe cases of diabetic retinopathy among diabetes patients.published_or_final_versio