Object localization in an image is usually handled by searching for an optimal subwindow that tightly covers the object of interest. However, the subwindows considered in previous work are limited to rectangles or other specified, simple shapes. With such specified shapes, no subwindow can cover the object of interest tightly. As a result, the desired subwindow around the object of interest may not be optimal in terms of the localization objective function, and cannot be detected by a subwindow search algorithm. In this paper, we propose a new graph-theoretic approach for object localization by searching for an optimal subwindow without pre-specifying its shape. Instead, we require the resulting subwindow to be well aligned with edge pixels that are detected from the image. This requirement is quantified and integrated into the localization objective function based on the widely-used bag of visual words technique. We show that the ratio-contour graph algorithm can be adapted to find the optimal free-shape subwindow in terms of the new localization objective function. In the experiment, we test the proposed approach on the PASCAL VOC 2006 and VOC 2007 databases for localizing several categories of animals. We find that its performance is better than the previous efficient subwindow search algorithm.

Accurately identifying corresponded landmarks from a population of shape instances is the major challenge in constructing statistical shape models. In this paper, we address this landmark-based shape-correspondence problem for 3D cases by developing a highly efficient landmark-sliding algorithm. This algorithm is able to quickly refine all the landmarks in a parallel fashion by sliding them on the 3D shape surfaces. We use 3D thin-plate splines to model the shape-correspondence error so that the proposed algorithm is invariant to affine transformations and more accurately reflects the nonrigid biological shape deformations between different shape instances. In addition, the proposed algorithm can handle both open-and closed-surface shape, while most of the current 3D shape-correspondence methods can only handle genus-0 closed surfaces. We conduct experiments on 3D hippocampus data and compare the performance of the proposed algorithm to the state-of-the-art MDL and SPHARM methods. We find that, while the proposed algorithm produces a shape correspondence with a better or comparable quality to the other two, it takes substantially less CPU time. We also apply the proposed algorithm to correspond 3D diaphragm data which have an open-surface shape.