An interpretation for probabilistic relaxation

doi:10.1016/0734-189X(83)90083-X

Computer Vision, Graphics, and Image Processing

Volume 22, Issue 3, June 1983, Pages 388-395

Computer Vision, Gra...

https://doi.org/10.1016/0734-189X(83)90083-X Get rights and content

Abstract

Probabilistic relaxation has been the basis of one of the popular cooperative processing mechanisms used in image analysis. It has been a mechanism whose theory has not been well understood. In this paper, some general conditional independence conditions are stated which give probabilistic relaxation the interpretation that each iteration computes the conditional probability of each local label given a new context which is the context of the previous iteration enlarged by one neighborhood width. This interpretation implies that relaxation iterations must only continue until the conditional independence assumptions no longer hold, or until the entire context is taken into account, whichever comes first.

References (6)

HaralickR.M. et al.
Compatibilities and the fixed points of arithmetic relaxation processes
Computer Graphics and Image Processing
(1980)
KirbyR.L.
A product rule relaxation method
Computer Graphics and Image Processing
(1980)
PelegS.
A new probabilistic relaxation scheme
IEEE Trans. Pattern Anal. Mach. Intelligence
(1980)

There are more references available in the full text version of this article.

Cited by (23)

Probabilistic relaxation labelling using the Fokker-Planck equation
2008, Pattern Recognition
In this paper we develop a new formulation of probabilistic relaxation labelling using the theory of diffusion processes on graphs. Our aim is to tackle the problem of labelling objects consistently and unambiguously using information concerning label consistency and initial label probabilities. We abstract this problem using a support graph with each graph node an object-label assignment. Initial object-label probabilities then evolve across the graph under the governance of the Fokker–Planck equation in terms of an infinitesimal generator matrix computed from the edge weights of the support graph. In this way we effectively kernelise probabilistic relaxation. Encouraging results are obtained in applying the new relaxation process in the applications of scene labelling, data classification, and feature correspondence matching.
Probabilistic relaxation and the Hough transform
2000, Pattern Recognition
We discuss the recent developments in probabilistic relaxation which is used as a tool for contextual sensory data interpretation. The relationship of this technique with the Hough transform is then established, focusing on the Generalised Hough Transform (GHT). We show that the label probability updating formula of the probabilistic relaxation process exploiting binary relations between object primitives, under the assumption that the primitives convey weak context, exhibits very close similarity to the voting function employed by a computationally efficient GHT. We argue that the relationship could be exploited by importing the positive features of the respective techniques to benefit one another. Specific suggestions for enhancing the respective techniques are mentioned. They include the adoption of the representational efficiency of the Hough transform to reduce the computational complexity of probabilistic relaxation. Vice versa, in the case of the Generalised Hough transform it is pointed out that the effect of an unknown object transformation could be dealt with by means of a parallel cooperative interpretation rather than by means of an exhaustive search through the parameter space of a transformation group. This has implications in terms of both the storage and computational requirements of the GHT. It also opens the possibility of using the GHT for detecting objects subject to more complex transformations such as affine or perspective. The relationship also suggests the possibility of using alternative voting functions which may speed up the object detection process.
Color Image Segmentation for Bladder Cancer Diagnosis
1998, Mathematical and Computer Modelling
In this paper, a new color image segmentation method is proposed to extract the region of bladder tumor from a color bladder image. In the past, the diagnosis of bladder tumors mainly relies upon cystoscopic examination with an in vivo staining technique. This manner heavily depends on the interpreter's experience and often results in errors in diagnosis. Instead of previous method, we use methylene blue in vivo staining combined with color segmentation techniques to improve the accuracy of the diagnosis of bladder tumors. The segmentation task can be decomposed into two stages. First, cluster detection combined with probabilistic relaxation is used to extract the clusters of specified colors from the HLS color space. Then, in order to refine the chromatic properties, the Bayesian algorithm is employed to reject the false region from the clusters obtained in the first stage. Experimental results show that the proposed method can segment the bladder tumor successfully. The technique could serve as an auxiliary tool for doctors or researchers in the diagnosis of bladder tumors.
A relaxation scheme for improving a convexity based clustering method
1994, Pattern Recognition Letters
A fuzzy logic and neural network approach to boundary detection for noisy imagery
1994, Fuzzy Sets and Systems
In this paper, an edge relaxation method utilizing fuzzy logic and neural networks is presented. The goal is to extract physically meaningful edge segments. The candidates for edge segments are first estimated using a local derivative operator with a window of small size. To enhance the performance of edge detection, in addition to the output of a derivative operator, the spatial relationships among the neighboring edge segments around an edge segment of interest are used as additional source of information. Fuzzy rules, each of which is associated with a neighborhood pattern defined by the spatial relationships among the neighboring edge segments, are used as a computational framework of collecting the evidence for the existence of an edge segment. These fuzzy rules are trained by a specially structured neural network which performs fuzzy reasoning operation. Through a series of experiments, the proposed edge relaxation scheme is found to exhibit reasonable performance of eliminating false edges, strengthening weak real edges and bridging small gaps between edge segments on object boundary.
A syntactic approach to time-varying pattern analysis
1992, Information Sciences
A syntactic method for the analysis of time-varying (TV) patterns is presented. The TV phenomena is analyzed using a language translation schema. Stochastic tree grammars are used to describe the patterns at each stage of the TV image sequence and the stochastic translation schema is used to model the evolution process of the TV image sequence. It is shown that the necessary conditions for the existence of a matched filter are preserved under the proposed stochastic translation, and a spatial matched filter Ψ_s can be designed for the patterns at each stage of the image sequence. In addition, we show that a temporal matched filter Ψ_t can also be designed for the trajectories formed by the pattern primitives in the image sequence. These filters can iteratively extract the contextual information from the spatial context and the temporal context in a pattern, respectively. They form a trade-off to each other, but they can not be completely replaced by each other. This is demonstrated by an experiment.

View all citing articles on Scopus

View full text

NoteAn interpretation for probabilistic relaxation

Abstract

Computer Graphics and Image Processing

Computer Graphics and Image Processing

A new probabilistic relaxation scheme

IEEE Trans. Pattern Anal. Mach. Intelligence

Note
An interpretation for probabilistic relaxation