IntroductionMost segment based stereo methods estimate disparity by modeling color segments as 3-D planes [2]. Inherently, such methods are sensitive to segmentation parameters and intolerant to segmentation errors. Two main dependencies of these methods on the underlying segmentation algorithm are: size of segments used for estimating planes, and assignment of a single plane to the whole segment. Specifically, in the case of under-segmentation, there is a higher chance of merging multiple objects (with multiple plane surfaces) into a single segment. Consequently, planes estimated using these segments are erroneous. The effect propagates to the disparity map, wherein a larger segment encompassing multiple objects is incorrectly represented by a single disparity plane. In the over-segmentation case, which gives smaller color segments, the estimated planes may be unreliable, leading to an inaccurate disparity map. Popular segment based methods try to solve this problem by re-fitting the planes on grouped segments, in an iterative manner [2]. We propose a novel algorithm for generating sub-pixel accurate disparities on a perpixel basis, thus alleviating the problems arising from methods that estimate disparities on a per-segment basis. The proposed method computes sub-pixel precision disparity maps using the recent minimum spanning tree (MST) [4] based cost aggregation framework. Since the disparity at every pixel is modeled by a plane equation, the goal is to ensure that all pixels belonging to a planar surface are labeled with the same plane equation. We show that using a reduced and refined set of planes as candidate labels in the aggregation framework ensures homogeneous labeling within a color segment. Proposed MethodOur method computes an initial set of plane equations (label set) by fitting planes inside a color segment using the consistent disparities from an initial disparity map. The initial disparity map may be generated using any local or global algorithm. These plane equations form the initial label set and a matching cost volume is computed over this set for every pixel. This cost volume is aggregated using MST based cost aggregation framework and a WTA over the aggregated cost volume gives the initial labeling. The number of labels in the initial set is of the order of the number of segments, with a plane estimate for every segment. The initial labeling is used along with the color segmentation to filter and generate a reduced set of planes. This framework of plane filtering followed by re-labeling leads to a more accurate disparity map. In addition, segment analysis is also used to modify the plane matching cost. We weigh the pixel matching cost by a support factor, where the support factor is derived from the distribution of plane labels within the color segment, as follows:

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