A Latent Source Model for Patch-Based Image Segmentation
Despite the popularity and empirical success of patch-based nearest-neighbor and weighted majority voting approaches to medical image segmentation, there has been no theoretical development on when, why, and how well these nonparametric methods work. We b
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Abstract. Despite the popularity and empirical success of patch-based nearest-neighbor and weighted majority voting approaches to medical image segmentation, there has been no theoretical development on when, why, and how well these nonparametric methods work. We bridge this gap by providing a theoretical performance guarantee for nearestneighbor and weighted majority voting segmentation under a new probabilistic model for patch-based image segmentation. Our analysis relies on a new local property for how similar nearby patches are, and fuses existing lines of work on modeling natural imagery patches and theory for nonparametric classification. We use the model to derive a new patchbased segmentation algorithm that iterates between inferring local label patches and merging these local segmentations to produce a globally consistent image segmentation. Many existing patch-based algorithms arise as special cases of the new algorithm.
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Introduction
Nearest-neighbor and weighted majority voting methods have been widely used in medical image segmentation, originally at the pixel or voxel level [11] and more recently for image patches [2,6,10,12]. Perhaps the primary reason for the popularity of these nonparametric methods is that standard label fusion techniques for image segmentation require robust nonrigid registration whereas patch-based methods sidestep nonrigid image alignment altogether. Thus, patchbased approaches provide a promising alternative to registration-based methods for problems that present alignment challenges, as in the case of whole body scans or other applications characterized by large anatomical variability. A second reason for patch-based methods’ growing popularity lies in their efficiency of computation: fast approximate nearest-neighbor search algorithms, tailored for patches [3] and for high-dimensional spaces more generally (e.g., [1,9]), can rapidly find similar patches, and can readily parallelize across search queries. For problems where the end goal is segmentation or a decision based on segmentation, solving numerous nonrigid registration subproblems required for standard label fusion could be a computationally expensive detour that, even if successful, might not produce better solutions than a patch-based approach. Many patch-based image segmentation methods can be viewed as variations of the following simple algorithm. To determine whether a pixel in the new image should be foreground (part of the object of interest) or background, we consider c Springer International Publishing Switzerland 2015 N. Navab et al. (Eds.): MICCAI 2015, Part III, LNCS 9351, pp. 140–148, 2015. DOI: 10.1007/978-3-319-24574-4_17
Patch-Based Image Segmentation
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the patch centered at that pixel. We compare this image patch to patches in a training database, where each training patch is labeled either foreground or background depending on the pixel at the center of the training patch. We transfer the label from the closest patch in the training database to the pixel of interest in the new image. A pleth
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