The primary goal of pattern recognition is supervised or unsupervised classification. Among the various frameworks in which pattern recognition has been traditionally formulated, the statistical approach has been most intensively studied and used in practice. More recently, neural network techniques and methods imported from statistical learning theory have been receiving increasing attention. The design of a recognition system requires careful attention to the following issues: definition of pattern classes, sensing environment, pattern representation, feature extraction and selection, cluster analysis, classifier design and learning, selection of training and test samples, and performance evaluation. In spite of almost 50 years of research and development in this field, the general problem of recognizing complex patterns with arbitrary orientation, location, and scale remains unsolved. New and emerging applications, such as data mining, web searching, retrieval of multimedia data, face recognition, and cursive handwriting recognition, require robust and efficient pattern recognition techniques. The objective of this review paper is to summarize and compare some of the well-known methods used in various stages of a pattern recognition system and identify research topics and applications which are at the forefront of this exciting and challenging field.

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Statistical pattern recognition: a review

This paper addresses the problem of segmenting an image into regions. We define a predicate for measuring the evidence for a boundary between two regions using a graph-based representation of the image. We then develop an efficient segmentation algorithm based on this predicate, and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties. We apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph, and illustrate the results with both real and synthetic images. The algorithm runs in time nearly linear in the number of graph edges and is also fast in practice. An important characteristic of the method is its ability to preserve detail in low-variability image regions while ignoring detail in high-variability regions.

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Efficient Graph-Based Image Segmentation

Many underlying relationships among data in several areas of science and engineering, e.g., computer vision, molecular chemistry, molecular biology, pattern recognition, and data mining, can be represented in terms of graphs. In this paper, we propose a new neural network model, called graph neural network (GNN) model, that extends existing neural network methods for processing the data represented in graph domains. This GNN model, which can directly process most of the practically useful types of graphs, e.g., acyclic, cyclic, directed, and undirected, implements a function tau(G,n) isin IRm that maps a graph G and one of its nodes n into an m-dimensional Euclidean space. A supervised learning algorithm is derived to estimate the parameters of the proposed GNN model. The computational cost of the proposed algorithm is also considered. Some experimental results are shown to validate the proposed learning algorithm, and to demonstrate its generalization capabilities.

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The Graph Neural Network Model

We develop a common theoretical framework for combining classifiers which use distinct pattern representations and show that many existing schemes can be considered as special cases of compound classification where all the pattern representations are used jointly to make a decision. An experimental comparison of various classifier combination schemes demonstrates that the combination rule developed under the most restrictive assumptions-the sum rule-outperforms other classifier combinations schemes. A sensitivity analysis of the various schemes to estimation errors is carried out to show that this finding can be justified theoretically.

On combining classifiers

Registration is a fundamental task in image processing used to match two or more pictures taken, for example, at different times, from different sensors, or from different viewpoints. Virtually all large systems which evaluate images require the registration of images, or a closely related operation, as an intermediate step. Specific examples of systems where image registration is a significant component include matching a target with a real-time image of a scene for target recognition, monitoring global land usage using satellite images, matching stereo images to recover shape for autonomous navigation, and aligning images from different medical modalities for diagnosis.Over the years, a broad range of techniques has been developed for various types of data and problems. These techniques have been independently studied for several different applications, resulting in a large body of research. This paper organizes this material by establishing the relationship between the variations in the images and the type of registration techniques which can most appropriately be applied. Three major types of variations are distinguished. The first type are the variations due to the differences in acquisition which cause the images to be misaligned. To register images, a spatial transformation is found which will remove these variations. The class of transformations which must be searched to find the optimal transformation is determined by knowledge about the variations of this type. The transformation class in turn influences the general technique that should be taken. The second type of variations are those which are also due to differences in acquisition, but cannot be modeled easily such as lighting and atmospheric conditions. This type usually effects intensity values, but they may also be spatial, such as perspective distortions. The third type of variations are differences in the images that are of interest such as object movements, growths, or other scene changes. Variations of the second and third type are not directly removed by registration, but they make registration more difficult since an exact match is no longer possible. In particular, it is critical that variations of the third type are not removed. Knowledge about the characteristics of each type of variation effect the choice of feature space, similarity measure, search space, and search strategy which will make up the final technique. All registration techniques can be viewed as different combinations of these choices. This framework is useful for understanding the merits and relationships between the wide variety of existing techniques and for assisting in the selection of the most suitable technique for a specific problem.

A survey of image registration techniques

1: Introduction.- 1.1 Graphics, Image Processing, and Pattern Recognition.- 1.2 Forms of Pictorial Data.- 1.2.1 Class 1: Full Gray Scale and Color Pictures.- 1.2.2 Class 2: Bilevel or "Few Color" pictures.- 1.2.3 Class 3: Continuous Curves and Lines.- 1.2.4 Class 4: Points or Polygons.- 1.3 Pictorial Input.- 1.4 Display Devices.- 1.5 Vector Graphics.- 1.6 Raster Graphics.- 1.7 Common Primitive Graphic Instructions.- 1.8 Comparison of Vector and Raster Graphics.- 1.9 Pictorial Editor.- 1.10 Pictorial Transformations.- 1.11 Algorithm Notation.- 1.12 A Few Words on Complexity.- 1.13 Bibliographical Notes.- 1.14 Relevant Literature.- 1.15 Problems.- 2: Digitization of Gray Scale Images.- 2.1 Introduction.- 2.2 A Review of Fourier and other Transforms.- 2.3 Sampling.- 2.3.1 One-dimensional Sampling.- 2.3.2 Two-dimensional Sampling.- 2.4 Aliasing.- 2.5 Quantization.- 2.6 Bibliographical Notes.- 2.7 Relevant Literature.- 2.8 Problems.- Appendix 2.A: Fast Fourier Transform.- 3: Processing of Gray Scale Images.- 3.1 Introduction.- 3.2 Histogram and Histogram Equalization.- 3.3 Co-occurrence Matrices.- 3.4 Linear Image Filtering.- 3.5 Nonlinear Image Filtering.- 3.5.1 Directional Filters.- 3.5.2 Two-part Filters.- 3.5.3 Functional Approximation Filters.- 3.6 Bibliographical Notes.- 3.7 Relevant Literature.- 3.8 Problems.- 4: Segmentation.- 4.1 Introduction.- 4.2 Thresholding.- 4.3 Edge Detection.- 4.4 Segmentation by Region Growing.- 4.4.1 Segmentation by Average Brightness Level.- 4.4.2 Other Uniformity Criteria.- 4.5 Bibliographical Notes.- 4.6 Relevant Literature.- 4.7 Problems.- 5: Projections.- 5.1 Introduction.- 5.2 Introduction to Reconstruction Techniques.- 5.3 A Class of Reconstruction Algorithms.- 5.4 Projections for Shape Analysis.- 5.5 Bibliographical Notes.- 5.6 Relevant Literature.- 5.7 Problems.- Appendix 5.A: An Elementary Reconstruction Program.- 6: Data Structures.- 6.1 Introduction.- 6.2 Graph Traversal Algorithms.- 6.3 Paging.- 6.4 Pyramids or Quad Trees.- 6.4.1 Creating a Quad Tree.- 6.4.2 Reconstructing an Image from a Quad Tree.- 6.4.3 Image Compaction with a Quad Tree.- 6.5 Binary Image Trees.- 6.6 Split-and-Merge Algorithms.- 6.7 Line Encodings and the Line Adjacency Graph.- 6.8 Region Encodings and the Region Adjacency Graph.- 6.9 Iconic Representations.- 6.10 Data Structures for Displays.- 6.11 Bibliographical Notes.- 6.12 Relevant Literature.- 6.13 Problems.- Appendix 6.A: Introduction to Graphs.- 7: Bilevel Pictures.- 7.1 Introduction.- 7.2 Sampling and Topology.- 7.3 Elements of Discrete Geometry.- 7.4 A Sampling Theorem for Class 2 Pictures.- 7.5 Contour Tracing.- 7.5.1 Tracing of a Single Contour.- 7.5.2 Traversal of All the Contours of a Region.- 7.6 Curves and Lines on a Discrete Grid.- 7.6.1 When a Set of Pixels is not a Curve.- 7.6.2 When a Set of Pixels is a Curve.- 7.7 Multiple Pixels.- 7.8 An Introduction to Shape Analysis.- 7.9 Bibliographical Notes.- 7.10 Relevant Literature.- 7.11 Problems.- 8: Contour Filling.- 8.1 Introduction.- 8.2 Edge Filling.- 8.3 Contour Filling by Parity Check.- 8.3.1 Proof of Correctness of Algorithm 8.3.- 8.3.2 Implementation of a Parity Check Algorithm.- 8.4 Contour Filling by Connectivity.- 8.4.1 Recursive Connectivity Filling.- 8.4.2 Nonrecursive Connectivity Filling.- 8.4.3 Procedures used for Connectivity Filling.- 8.4.4 Description of the Main Algorithm.- 8.5 Comparisons and Combinations.- 8.6 Bibliographical Notes.- 8.7 Relevant Literature.- 8.8 Problems.- 9: Thinning Algorithms.- 9.1 Introduction.- 9.2 Classical Thinning Algorithms.- 9.3 Asynchronous Thinning Algorithms.- 9.4 Implementation of an Asynchronous Thinning Algorithm.- 9.5 A Quick Thinning Algorithm.- 9.6 Structural Shape Analysis.- 9.7 Transformation of Bilevel Images into Line Drawings.- 9.8 Bibliographical Notes.- 9.9 Relevant Literature.- 9.10 Problems.- 10: Curve Fitting and Curve Displaying.- 10.1 Introduction.- 10.2 Polynomial Interpolation.- 10.3 Bezier Polynomials.- 10.4 Computation of Bezier Polynomials.- 10.5 Some Properties of Bezier Polynomials.- 10.6 Circular Arcs.- 10.7 Display of Lines and Curves.- 10.7.1 Display of Curves through Differential Equations.- 10.7.2 Effect of Round-off Errors in Displays.- 10.8 A Point Editor.- 10.8.1 A Data Structure for a Point Editor.- 10.8.2 Input and Output for a Point Editor.- 10.9 Bibliographical Notes.- 10.10 Relevant Literature.- 10.11 Problems.- 11: Curve Fitting with Splines.- 11.1 Introduction.- 11.2 Fundamental Definitions.- 11.3 B-Splines.- 11.4 Computation with B-Splines.- 11.5 Interpolating B-Splines.- 11.6 B-Splines in Graphics.- 11.7 Shape Description and B-splines.- 11.8 Bibliographical Notes.- 11.9 Relevant Literature.- 11.10 Problems.- 12: Approximation of Curves.- 12.1 Introduction.- 12.2 Integral Square Error Approximation.- 12.3 Approximation Using B-Splines.- 12.4 Approximation by Splines with Variable Breakpoints.- 12.5 Polygonal Approximations.- 12.5.1 A Suboptimal Line Fitting Algorithm.- 12.5.2 A Simple Polygon Fitting Algorithm.- 12.5.3 Properties of Algorithm 12.2.- 12.6 Applications of Curve Approximation in Graphics.- 12.6.1 Handling of Groups of Points by a Point Editor.- 12.6.2 Finding Some Simple Approximating Curves.- 12.7 Bibliographical Notes.- 12.8 Relevant Literature.- 12.9 Problems.- 13: Surface Fitting and Surface Displaying.- 13.1 Introduction.- 13.2 Some Simple Properties of Surfaces.- 13.3 Singular Points of a Surface.- 13.4 Linear and Bilinear Interpolating Surface Patches.- 13.5 Lofted Surfaces.- 13.6 Coons Surfaces.- 13.7 Guided Surfaces.- 13.7.1 Bezier Surfaces.- 13.7.2 B-Spline Surfaces.- 13.8 The Choice of a Surface Partition.- 13.9 Display of Surfaces and Shading.- 13.10 Bibliographical Notes.- 13.11 Relevant Literature.- 13.12 Problems.- 14: The Mathematics of Two-Dimensional Graphics.- 14.1 Introduction.- 14.2 Two-Dimensional Transformations.- 14.3 Homogeneous Coordinates.- 14.3.1 Equation of a Line Defined by Two Points.- 14.3.2 Coordinates of a Point Defined as the Intersection of Two Lines.- 14.3.3 Duality.- 14.4 Line Segment Problems.- 14.4.1 Position of a Point with respect to a Line.- 14.4.2 Intersection of Line Segments.- 14.4.3 Position of a Point with respect to a Polygon.- 14.4.4 Segment Shadow.- 14.5 Bibliographical Notes.- 14.6 Relevant Literature.- 14.7 Problems.- 15: Polygon Clipping.- 15.1 Introduction.- 15.2 Clipping a Line Segment by a Convex Polygon.- 15.3 Clipping a Line Segment by a Regular Rectangle.- 15.4 Clipping an Arbitrary Polygon by a Line.- 15.5 Intersection of Two Polygons.- 15.6 Efficient Polygon Intersection.- 15.7 Bibliographical Notes.- 15.8 Relevant Literature.- 15.9 Problems.- 16: The Mathematics of Three-Dimensional Graphics.- 16.1 Introduction.- 16.2 Homogeneous Coordinates.- 16.2.1 Position of a Point with respect to a Plane.- 16.2.2 Intersection of Triangles.- 16.3 Three-Dimensional Transformations.- 16.3.1 Mathematical Preliminaries.- 16.3.2 Rotation around an Axis through the Origin.- 16.4 Orthogonal Projections.- 16.5 Perspective Projections.- 16.6 Bibliographical Notes.- 16.7 Relevant Literature.- 16.8 Problems.- 17: Creating Three-Dimensional Graphic Displays.- 17.1 Introduction.- 17.2 The Hidden Line and Hidden Surface Problems.- 17.2.1 Surface Shadow.- 17.2.2 Approaches to the Visibility Problem.- 17.2.3 Single Convex Object Visibility.- 17.3 A Quad Tree Visibility Algorithm.- 17.4 A Raster Line Scan Visibility Algorithm.- 17.5 Coherence.- 17.6 Nonlinear Object Descriptions.- 17.7 Making a Natural Looking Display.- 17.8 Bibliographical Notes.- 17.9 Relevant Literature.- 17.10 Problems.- Author Index.- Algorithm Index.

Algorithms for Graphics and Image Processing

Structural Pattern Recognition

Piecewise approximation is described as a way of feature extraction, data compaction, and noise filtering of boundaries of regions of pictures and waveforms. A new fast algorithm is proposed which allows for a variable number of segments. After an arbitrary initial choice, segments are split or merged in order to drive the error norm under a prespecified bound. Results of computer experiments with cell outlines and electrocardiograms are reported.

Segmentation of Plane Curves

A method that combines region growing and edge detection for image segmentation is presented. The authors start with a split-and merge algorithm wherein the parameters have been set up so that an over-segmented image results. Region boundaries are then eliminated or modified on the basis of criteria that integrate contrast with boundary smoothness, variation of the image gradient along the boundary, and a criterion that penalizes for the presence of artifacts reflecting the data structure used during segmentation (quadtree in this case). The algorithms were implemented in the C language on a Sun 3/160 workstation running under the Unix operating system. Simple tool images and aerial photographs were used to test the algorithms. The impression of human observers is that the method is very successful on the tool images and less so on the aerial photograph images. It is thought that the success in the tool images is because the objects shown occupy areas of many pixels, making it is easy to select parameters to separate signal information from noise. >

Integrating region growing and edge detection

In the past, picture segmentation has been performed by merging small primitive regions or by recursively splitting the whole picture. This paper combines the two approaches with significant increase in processing speed while maintaining small memory requirements. The data structure is described in detail and examples of implementations are given.

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Theodosios Pavlidis

Papers

Algorithms for Graphics and Image Processing

Structural Pattern Recognition

Segmentation of Plane Curves

Integrating region growing and edge detection

Picture Segmentation by a Tree Traversal Algorithm