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Rajesh N. Davé and Kurra Bhaswan.
Adaptive Fuzzy c-Shells Clustering and Detection of Ellipses.
TNN,
3(5):643--662,
1992.
Keywords:
Clustering,
Fuzzy Clustering,
Image Data.
| Abstract: |
Several generalizations of the fuzzy c-shells (FCS) algorithm are presented for characterizing and detecting clusters that are hyperellipsoidal shells. An earlier generalization, called the Adaptive fuzzyz c-shells (AFCS) algorithm, is examined in details, and is found to have global convergence problems when the shapes to be detected are partial. New formulations are considered wherein the norm inducing matrix in the distance metric is unconstrained in contrast to the AFCS algorithm. The resulting algorithm, called the AFCS-U algorithm, is shown to perform better for partial shapes. Another formulation is also considered, which is based on the second-order quadrics equation, resulting in a linear system of equations. These algorithms are shown to be able to detect ellipses and circles in two-dimensional data. Their performance is compared with the Hough transform (HT) based methods for ellipse detection. Existing HT-based methods for ellipse detection are evaluated, and a multistage method incorporating the good features of all the methods is used for comparison. It is demonstrated through numerical examples of real image data that the AFCS algorithm requires less memory than the HT based methods, and it is at least an order of magnitude faster than the HT approach. It is also shown that the use of fuzy memberships improves the ability to attain global optima compared with the use of hard memberships. |
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Konstantin B. Konstantinov and Toshiomi Yoshida.
Real-Time Qualitative Analysis of the Temporal Shapes of (Bio)process Variables.
AIChe,
38(11):1703--1715,
1992.
Keywords:
Temporal Reasoning.
| Abstract: |
One of the limitations of today's knowledge-based (KB) systems for diagnostics and supervision is a lack of adequate temporal reasoning mechanisms. Most of these systemsare designed primarily to operate with the current values of the process variables and, sometimes, with their derivatives. Such simple capabilities, however, are not always sufficient to identify some complex dynamic phenomena, which in many cases leave their own unique ``stamp'' on the process behaviour, expressed in the form of characteristic temporal shapes of the related variables. To detect and diagnose adequately the events of interest, the KB system should be able to reason about the temporal shapes of the process variables. Although during manual supervision process operators rely heavily on such characteristic shapes as reliable symptoms of underlying phenomena, their exploitation has not been considered seriously by the designers of KB control systems. We propose a generic methodology for qualitative analysis of the temporal shapes of continuous process variables designed to be embedded into a real-time KB environment. It is applicable to bioprocesses, as well as to other complex dynamic systems. |
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Raghu Krishnapuram and Chih-Pin Freg.
Fitting an Unknown Number of Lines and Planes to Image Data through Compatible Cluster Merging.
PR,
25(4):385--400,
1992.
Keywords:
Cluster Validity Measures,
Image Data.
| Abstract: |
A compatible cluster merging algorithm is presented that is specially designed to find the optimum number of linear, planar and hyperplanar clusters (i.e.\ clusters that lie in a subspace of the original space), when an upper bound on the number of clusters present is known. This algorithm is shown to be superior to more traditional validity-measure-based approaches. The effectiveness and advantages of the proposed technique in 2D and 3D applications is demonstrated with both synthetic and real data. The proposed applications inlude character recognition, obtaining straight-line descriptions of intensity edge images and obtaining planar approximations of 3D (range) data. |
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Raghu Krishnapuram,
Olfa Nasraoui,
and Hichem Frigui.
The Fuzzy C Spherical Shells Algorithm: A New Approach.
TNN,
3(5):663--670,
1992.
Keywords:
Clustering,
Cluster Validity Measures.
| Abstract: |
The fuzzy c spherical shells (FCSS) algorithm is specially designed to search for clusters that can be described by circular arcs or, more generally, by shells of hyperspheres. In this paper, a new approach to the FCSS algorithm is presented. This algorithm is computationally and implementationally simpler than other clustering algorithms that have been suggested for this purpose. An unsupervisedalgorithm which automatically finds the optimum number of clusters is also proposed. This algorithm can be used when the number of clusters is not known. It uses a cluster validity measure to identify good clusters, merges all compatible clusters, and eliminates spurious clusters to achieve the final result. Experimental results on several data sets are presented. |
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Tony Lindeberg and Jan-Olof Eklundh.
Scale-space primal sketch: Construction and Experiments.
IVC,
10(1):3--18,
1992.
Keywords:
Multiscale Analysis,
Image Data.
| Abstract: |
We present a multi-scale representation of grey-level shape, called the scale-space primal sketch, that makes explicit features in scale-space as well as the relations between features at different levels of scale. The representation gives a qualitative description of the image structure -- stable scales and regions of interest -- in a solely bottom-up data-driven manner. Hence, it can be seen as preceding further processing, which can then be properly tuned. Experiments on real imagery demonstrate that the proposed theory gives intuitively reasonable results. |
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Stephane G. Mallat and Sifen Zhong.
Characterization of Signals from Multiscale Edges.
TPAMI,
14(7):710--732,
1992.
Keywords:
Wavelets,
Multiscale Analysis,
Image Data.
| Abstract: |
A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. We study the properties of multiscale edges through wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. We show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. We describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below our visual sensitivity. As an application, we implement a compact image coding algorithm that selects important edges and compresses the image data by factors over 30. |
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Mark J. Shensa.
The Discrete Wavelet Transform: Wedding the À Trous and Mallat Algorithms.
TSP,
40(10):2464--2484,
1992.
Keywords:
Wavelets,
Multiscale Analysis.
| Abstract: |
In a general sense this paper represents an effort to clarify the relationship of discrete and continuous wavelet transforms. More narrowly, it focuses on bringing together two separately motivated implementations of the wavelet transform, the {\sl algorithme \'a trous} and Mallat's multiresolution decomposition. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by one's choice of filters. In fact, the \'a trous algorithm, originally devised as a computationally efficient implementation, is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange \'a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. \newline A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computer the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Finally, relevant signal processing parameters are examined, and it it remarked that orthonormality is balanced by restrictions on resolution. |
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Padhraic Smyth and Rodney M. Goodman.
An Information Theoretic Approach to Rule Induction from Databases.
TKDE,
4(4):301--316,
1992.
Keywords:
Classification.
| Abstract: |
The knowledge acquisition bottleneck in obtaining rules directly from an expert is well known. Hence, the problem of {\sl automated} rule acquisition from data is a well-motivated one, particularily for domains where a database of sample data exists. In this paper, we introduce a novel algorithm for the induction of rules from examples. The algorithm is novel in the sense that it not only learns rules for a given concept (classification), but it simultaneously learns rules relating multiple concepts. This type of learning, known as generalized rule induction is considerably more general than existing algorithms which tend to be classification oriented. Initially we focus on the problem of determining a quantitative, well-defined rule preference measure. In particular, we propose a quantity called {\sl J-measure} as an information theoretic alternative to existing approaches. The J-measure quantifies the information content of a rule or a hypothesis. We will outline the information theoretic origins of this measure and examine its plausibility as a hypothesis preference measure. We then define the ITRULE algorithm which uses the newly proposed measure to learn a set of optimal rules from a set of data samples, and we conclude the paper with an analysis of experimental results on real-world data. |
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