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Richard J. Hathaway and James C. Bezdek.
Switching Regression Models and Fuzzy Clustering.
TFS,
1(3):195--204,
1993.
Keywords:
Clustering,
Fuzzy Clustering,
Regression.
| Abstract: |
A family of objective functions, called fuzzy c-regression models, is presented which can be used to fit switching regression models to certain types of mixed data. Minimization of particular objective functions in the family yields simultaneous estimates for the parameters of $c$ regression models, together with a fuzzy $c$-partitioning of the data. A general optimization approach for the family of objective functions is given and corresponding theoretical convergence results are discussed. We illustrate the new approach with two numerical examples that show how it can be used to fit mixed data to coupled linear and nonlinear models. |
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Raghu Krishnapuram and Ling-Fan Chen.
Implementation of Parallel Thinning Algorithms Using Recurrent Neural Networks.
TNN,
4(1):142--147,
1993.
Keywords:
Neural Networks,
Image Data.
| Abstract: |
In this paper we investigate the use of recurrent neural networks for skeletonization and thinning of binary images. The networks are trained to learn a deletion rule and they iteratively delete object pixels until only the skeleton remains. We present recurrent neural network architectures that implement a variety of thinning algorithms such as the Rosenfeld-Kak (RK) algorithm and the Wang-Zhang (WZ) algorithm. We also introduce a modified WZ algorithm which produces skeletons that are intuitively more pleasing. |
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Raghu Krishnapuram,
Hichem Frigui,
and Olfa Nasraoui.
The Fuzzy C Quadric Shell clustering algorithm and the detection of second-degree curves.
PRL,
14:545--552,
1993.
Keywords:
Clustering,
Fuzzy Clustering.
| Abstract: |
This paper introduces a new fuzzy clustering algorithm called the Fuzzy C Quadric Shell clustering algorithm which is expressly designed to seek clusters that can be described by segments of second-degree curves, or more generally by segments of shells of hyperquadrics. |
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Raghu Krishnapuram and James M. Keller.
A Possibilistic Approach to Clustering.
TFS,
1(2):98--110,
1993.
Keywords:
Clustering,
Fuzzy Clustering,
Fuzzy c-Means.
| Abstract: |
Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required in each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only volume clusters, but also clusters which are actually ``thin shells'', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from the fuzzy c-means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to 1. The constraint was used to generate the membership update equations for an iterative algorithm. The memberships resulting from FCM and its derivatives, however, do not always correspond to the intuitive concept of degree of belonging or compatibility. Moreover, the algorithms have considerably trouble in noisy environments. In this paper, we cast the clustering problem into the framework of possibility theory. Our approach differs from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes, i.e., the compatibilities of the points with the class prototypes. We construct an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derive the membership and prototype update equations from necessary conditions for minimization of our criterion function. We illustrate the advantages of the resulting family of possibilistic algorithms with several examples. |
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J. Lee and S. Chae.
Analysis on function duplicating capabilities of fuzzy controllers.
FSS,
56:127--143,
1993.
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Tony Lindeberg.
Effective Scale: A Natural Unit for Measuring Scale-Space Lifetime.
TPAMI,
15(10):1068--1074,
1993.
Keywords:
Noise Handling,
Multiscale Analysis.
| Abstract: |
The article develops a manner in which a notion of effective scale can be introduced in a formal way. For continuous signals, a scaling argument directly gives that a natural unit for measuring scale-space lifetime is in terms of the logarithm of the ordinary scale parameter. That approach is, however, not appropriate for discrete signals since then, an infinite lifetime would be assigned to structures existing in the original signal. Here, it is shown how such an effective scale parameter can be defined to give consistent results for both discrete and continuout signals. The treatment is based on the assumption that the probability that a local extremum disappears during a short-scale interval should not vary with scale. As a tool for the analysis, estimates are given of how the density of local extrema can be expected to vary with scale in the scale-space representation of different random noise signals both in the continuous and discrete cases. |
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Tony Lindeberg.
Detecting Salient Blob-Like Image Structures and Their Scales with a Scale-Space Primal Sketch: A Method for Focus-of-Attention.
IJCV,
11(3):283--318,
1993.
Keywords:
Classification,
Multiscale Analysis,
Image Data.
| Abstract: |
This article presents: (i) a multi-scale representation of grey-level shape called the scale-space primal sketch, which makes explicit both features in scale-space and the relations between structures at different scales, (ii) a methodology for extracting significant blob-like image structures from this representations, and (iii) applications to edge detection, histogram analysis, and junction classification demonstrating how the proposed method can be used for guiding later stage visual processes. \newline The representation gives a qualitative description of image structure, which allows for detection of stable scales and associated regions of interest in a solely bottom-up data-driven way. In other words, it generates coarse segmentation cues, and can hence be seen as preceding further processing, which can then be properly tuned. It is argued that once such information is available, many other processing tasks can become much simpler. Experiments on real imagery demonstrate that the proposed theory gives intuitive results. |
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