Pattern Recognition, Vol. 22, No. 1, pp. 21 28, 1989. Printed in Great Britain 0031 3203/89 $3.00 + .00 Pergamon Press plc Pattern Recognition Society A PARALLEL ALGORITHM FOR DETERMINING TWO-DIMENSIONAL OBJECT POSITIONS USING INCOMPLETE INFORMATION ABOUT THEIR BOUNDARIES AMIR A. AMINI,TERRY E. WEYMOUTH* and DAVIDJ. ANDERSON Department of Electrical Engineering and Computer Science,University of Michigan, Ann Arbor, MI 48109-2212, U.S.A. (Received 23 October 1987) Abstract--Extraction of two-dimensional object locations using current techniques is a computationally intensive process. In this paper a parallel algorithm is presented that can specifythe location of objects from edge streaks produced by an edge operator. Best-firstsearches are carried out in a number of non-interacting and localized edge streak spaces. The outcome of each search is a hypothesis. Each edge streak votes for a single hypothesis; it may also take part in the formation of other hypotheses. A poll of the votes determined the stronger hypotheses. The algorithm can be used as a front end to a visual pattern recognition system where features are extracted from the hypothesized object boundary or from the area localized by the hypothesized boundary. Experimental results from a biomedical domain are presented. Computer vision Two-dimensional object recognition Search Automated histopathology Edge-linking Model-based recognition Parallel algorithm Feature-learning 1. INTRODUCTION The boundaries of objects often provide important features in recognition and classification of visual patterns. Examples include industrial and biomedical applications. In industrial applications, parts are generally assumed to be fiat, that is, one of the dimensions is small compared to the other two. The methodology is to match features of the object boundary model against the features of the object boundaries in the image. The closest match in the sense of a metric space is then chosen as having the desired shape (partial occlusion is thus dealt with in some cases). The algorithm developed by Perkins,tn for example, is based on cross-correlating the tangent angle or the curvature as functions of the curve length between the scene description and the database of models. More recently, the algorithms proposed by Turney12) and Gottschalk 131 improve on the time complexity of the previous results. Turney uses salient features of object boundaries for matching. Gottschalk et al. reduce the dimension of the feature vectors by projecting them onto a subspace by the Karhunen- Lo6ve transform before the actual matching. For a thorough review of relevant work relating to two- dimensional object recognition the interested reader is referred to Turney(2) and KnollJ4t * To whom correspondence should be addressed. 21 In biomedical applications, a system designer has limited control over the environment and thus the problem of extracting object positions and contours still remains to be solved before pattern recognition and classification algorithms may be employed. Examples from biomedical applications include locating tumors in chest radiographs, finding boun- daries of white blood cells in images, extraction of left ventricular outlines from serial angiocardiograms, extraction of lung outlines from digitized chest X-rays, recognition of muscle cells and the recognition of inner-ear hair cells in grey-level images. The latter application has been the primary motivation underly- ing the work reported here. It is expected that the results, however, are of much wider applicability. Application of various operators to raw image data yields primitive edge elements. However, in non- controlled environments in many instances, discon- nected or spurious edge elements result due to noise in the data or inaccuracies of the operators. The resulting edge elements are relatively featureless; hence, addi- tional processing must be done for grouping edge elements (or edge streaks) into structures better suited to the process of interpretation. Several methods exist for extraction of contours from images. The Hough transform has been used to detect boundaries of shapes which can be specified using a small number of parameters. Kimme et al. ~51 have used the Hough technique for locating tumors which have circular shapes in chest radiographs. In the