We present an algorithm for detecting multiple rotational symmetries in natural images. Given an image, its gradient magnitude field is computed, and information from the gradients is spread using a diffusion process in the form of a gradient vector flow (GVF) field. We construct a graph whose nodes correspond to pixels in tire image, connecting points that are likely to be rotated versions of one another The n-cycles present in tire graph are made to vote for C/sub n/ symmetries, their votes being weighted by the errors in transformation between GVF in the neighborhood of the voting points, and the irregularity of the n-sided polygons formed by the voters. The votes are accumulated at tire centroids of possible rotational symmetries, generating a confidence map for each order of symmetry. We tested the method with several natural images.

This paper presents an approach for extending the normalized-cut (n-cut) segmentation algorithm to find symmetric regions present in natural images. We use an existing algorithm to quickly detect possible symmetries present in an image. The detected symmetries are then individually verified using the modified n-cut algorithm to eliminate spurious detections. The weights of the n-cut algorithm are modified so as to include both symmetric and spatial affinities. A global parameter is defined to model the tradeoff between spatial coherence and symmetry. Experimental results indicate that symmetric quality measure for a region segmented by our algorithm is a good indicator for the significance of the principal axis of symmetry.

This paper addresses the problem of detecting axes of bilateral symmetry in images. In order to achieve robustness to variation in illumination, only edge-gradient information is used. To overcome the problem of edge breaks, a potential field is developed from the edge map which spreads the information in the image plane. Pairs of points in the image plane are made to vote for their axes of symmetry with some confidence values. To make the method robust to overlapping objects, only local features in the form of Taylor coefficients are used for quantifying symmetry. We define an axis of symmetry histogram, which is used to accumulate the weighted votes for all possible axes of symmetry. To reduce the computational complexity of voting, a hashing scheme is proposed, wherein pairs of points, whose potential fields are too asymmetric, are pruned by not being counted for the vote. Experimental results indicate that the proposed method is fairly robust to edge breaks and is able to detect symmetries even when only 0.05% of the possible pairs are used for voting.

We present a novel vector quantization method for pattern classification tasks. The input space is quantized into volume regions by code-vectors formed by weights of neurons. During training, the volume regions are merged and split, depending upon the ambiguity in classification, measured using Kullback-Leibler divergence. The heuristic followed is to split ambiguous regions, and merge two volume regions if they contain predominant populations of the same class. The neural network forms a generalized Delaunay graph, whose topology changes dynamically with the merging and splitting. The simulation results indicate the utility of the proposed method.