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Normalized Cuts and Image Segmentation Jianbo Shi and Jitendra Malik, Member , IEEE Abstract —We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut , for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images, as well as motion sequences, and found the results to be very encouraging. Index Terms —Grouping, image segmentation, graph partitioning. æ 1I NTRODUCTION N EARLY 75 years ago, Wertheimer [24] pointed out the importance of perceptual grouping and organization in vision and listed several key factors, such as similarity, proximity, and good continuation, which lead to visual grouping. However, even to this day, many of the computational issues of perceptual grouping have re- mained unresolved. In this paper, we present a general framework for this problem, focusing specifically on the case of image segmentation. Since there are many possible partitions of the domain I of an image into subsets, how do we pick the “right” one? There are two aspects to be considered here. The first is that there may not be a single correct answer. A Bayesian view is appropriate—there are several possible interpretations in the context of prior world knowledge. The difficulty, of course, is in specifying the prior world knowledge. Some of it is low level, such as coherence of brightness, color, texture, or motion, but equally important is mid- or high- level knowledge about symmetries of objects or object models. The second aspect is that the partitioning is inherently hierarchical. Therefore, it is more appropriate to think of returning a tree structure corresponding to a hierarchical partition instead of a single “flat” partition. This suggests that image segmentation based on low- level cues cannot and should not aim to produce a complete final “correct” segmentation. The objective should instead be to use the low-level coherence of brightness, color, texture, or motion attributes to sequentially come up with hierarchical partitions . Mid- and high-level knowledge can be used to either confirm these groups or select some for further attention. This attention could result in further repartition- ing or grouping. The key point is that image partitioning is to be done from the big picture downward, rather like a painter first marking out the major areas and then filling in the details.
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