Linda G. Shapiro

Structural Descriptions and Inexact Matching

In this paper we formally define the structural description of an object and the concepts of exact and inexact matching of two structural descriptions. We discuss the problems associated with a brute-force backtracking tree search for inexact matching and develop several different algorithms to make the tree search more efficient. We develop the formula for the expected number of nodes in the tree for backtracking alone and with a forward checking algorithm. Finally, we present experimental results showing that forward checking is the most efficient of the algorithms tested.

The Consistent Labeling Problem: Part II

In this first part of a two-part paper we introduce a general consistent labeling problem based on a unit constraint relation T containing N-tuples of units which constrain one another, and a compatibility relation R containing N-tuples of unit-label pairs specifying which N-tuples of units are compatible with which N-tuples of labels. We show that Latin square puzzles, finding N-ary relations, graph or auto-mata homomorphisms, graph colorings, as well as determining satisfiability of propositional logic statements and solving scene and edge labeling problems, are all special cases of the general consistent labeling problem. We then discuss the various approaches that researchers have used to speed up the tree search required to find consistent labelings. Each of these approaches uses a particular look-ahead operator to help eliminate backtracking in the tree search. Finally, we define the ¿KP two-parameter class of look-ahead operators which includes, as special cases, the operators other researchers have used.

A new connected components algorithm for virtual memory computers

Abstract A new algorithm for calculating the connected components of a binary image is presented, and a proof of correctness is given. For a large image, this algorithm required 1 hour of CPU time while the standard technique used over 36 hours. The storage requirements for this new algorithm are appropriate for small minicomputers as well as for larger machines.

Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering

This paper describes a technique for transforming a twodimensional shape into a binary relation whose clusters represent the intuitively pleasing simple parts of the shape. The binary relation can be defined on the set of boundary points of the shape or on the set of line segments of a piecewise linear approximation to the boundary. The relation includes all pairs of vertices (or segments) such that the line segment joining the pair lies entirely interior to the boundary of the shape. The graph-theoretic clustering method first determines dense regions, which are local regions of high compactness, and then forms clusters by merging together those dense regions having high enough overlap. Using this procedure on handdrawn colon shapes copied from an X-ray and on handprinted characters, the parts determined by the clustering often correspond well to decompositions that a human might make.

A Structural Model of Shape

Shape description and recognition is an important and interesting problem in scene analysis. Our approach to shape description is a formal model of a shape consisting of a set of primitives, their properties, and their interrelationships. The primitives are the simple parts and intrusions of the shape which can be derived through the graph-theoretic clustering procedure described in [31]. The interrelationships are two ternary relations on the primitives: the intrusion relation which relates two simple parts that join to the intrusion they surround and the protrusion relation which relates two intrusions to the protrusion between them. Using this model, a shape matching procedure that uses a tree search with look-ahead to find mappings from a prototype shape to a candidate shape has been developed. An experimental Snobol4 implementation has been used to test the program on hand-printed character data with favorable results.

Organization of Relational Models for Scene Analysis

Relational models are commonly used in scene analysis systems. Most such systems are experimental and deal with only a small number of models. Unknown objects to be analyzed are usually sequentially compared to each model. In this paper, we present some ideas for organizing a large database of relational models. We define a simple relational distance measure, prove it is a metric, and using this measure, describe two organizational/access methods: clustering and binary search trees. We illustrate these methods with a set of randomly generated graphs.

Matching Three-Dimensional Objects Using a Relational Paradigm

Abstract A relational model for describing three-dimensional objects has been designed and implemented. The model, which provides a rough description to be used at the top level of a hierarchy for describing objects, was designed for initial matching attempts on an unknown object. Each description is in terms of the set of simple parts of an object. Simple parts can be sticks (long, thin parts), plates (flat, wide parts) and blobs (parts that have three significant dimensions). The relations include an attribute-value table for global properties of the object, the properties of the simple parts, binary connection and support relationships, ternary connection relationships, parallel relationships, perpendicular relationships and binary constraints. An important use of the model is to characterize the similarity and differences between three-dimensional objects. Toward this end, we have defined a measure of relational similarity between three-dimensional object models and a measure of feature similarity, based only on Euclidean distance between attribute-value tables. In a series of computer tests, we compare the results of using the two different similarity measures and conclude that the relational similarity is much more powerful than the feature similarity and should be used when grouping the objects in the database for fast access.

Experiments in Segmentation Using a Facet Model Region Grower

Abstract A region growing scheme based upon the facet model (R. M. Haralick, Computer Graphics Image Processing 12, 1980, 60–73; R. M. Haralick and L. T. Watson Computer Graphics Image Processing 15, 1981, 113–129) is presented. The process begins with an initial segmentation which preserves much of the detailed resolution of the original image. Next a region property list and a region adhacency graph corresponding to the segmented image are constructed. Global information is then used to merge atomic regions. The region growing algorithm is based upon extensions of the facet model, but it is a higher-level algorithm which treats regions as primitive elements. The basic algorithm and several variations are described, including a version that uses a threshold on the amount a property vector is allowed to change to control the region growing process. The convergence of this thresholded facet iteration is also proved. Finally, the results of comparative experiments are presented.

Data structures for picture processing: A survey

Abstract A variety of algorithms have been invented for use in picture processing. An important aspect of the algorithms is the data structure(s) employed. A data structure may be chosen to represent a particular structural relationship, to save space, or to allow for fast access to data. This paper surveys four major classes of data structures used in current picture processing research and gives several examples of the use of each type of structure in particular algorithms or systems. The structures surveyed are linear lists hierarchic structures, graph structures, and recursive structures.

Identification of Space Curves from Two-Dimensional Perspective Views

This paper describes a new method to be used for matching three-dimensional objects with curved surfaces to two-dimensional perspective views. The method requires for each three-dimensional object a stored model consisting of a closed space curve representing some characteristic connected curved edges of the object. The input is a two-dimensional perspective projection of one of the stored models represented by an ordered sequence of points. The input is converted to a spline representation which is sampled at equal intervals to derive a curvature function. The Fourier transform of the curvature function is used to represent the shape. The actual matching is reduced to a minimization problem which is handled by the Levenberg-Marquardt algorithm [3].