Richard M Jiang

Arya A Pourzanjani, Richard M Jiang, Brian Mitchell et al.

We introduce an approach based on the Givens representation for posterior inference in statistical models with orthogonal matrix parameters, such as factor models and probabilistic principal component analysis (PPCA). We show how the Givens representation can be used to develop practical methods for transforming densities over the Stiefel manifold into densities over subsets of Euclidean space. We show how to deal with issues arising from the topology of the Stiefel manifold and how to inexpensively compute the change-of-measure terms. We introduce an auxiliary parameter approach that limits the impact of topological issues. We provide both analysis of our methods and numerical examples demonstrating the effectiveness of the approach. We also discuss how our Givens representation can be used to define general classes of distributions over the space of orthogonal matrices. We then give demonstrations on several examples showing how the Givens approach performs in practice in comparison with other methods.

Richard M Jiang

Saliency detection has been an intuitive way to provide useful cues for object detection and segmentation, as desired for many vision and graphics applications. In this paper, we provided a robust method for salient object detection and segmentation. Other than using various pixel-level contrast definitions, we exploited global image structures and proposed a new geodesic method dedicated for salient object detection. In the proposed approach, a new geodesic scheme, namely geodesic tunneling is proposed to tackle with textures and local chaotic structures. With our new geodesic approach, a geodesic saliency map is estimated in correspondence to spatial structures in an image. Experimental evaluation on a salient object benchmark dataset validated that our algorithm consistently outperformed a number of the state-of-art saliency methods, yielding higher precision and better recall rates. With the robust saliency estimation, we also present an unsupervised hierarchical salient object cut scheme simply using adaptive saliency thresholding, which attained the highest score in our F-measure test. We also applied our geodesic cut scheme to a number of image editing tasks as demonstrated in additional experiments.