Auto-completion of contours in sketches, maps and sparse 2D images based on topological persistence.

We design a new fast algorithm to automatically complete closed contours in a finite point cloud on the plane. The only input can be a scanned map with almost closed curves, a hand-drawn artistic sketch or any sparse dotted image in 2D without any extra parameters. The output is a hierarchy of closed contours that have a long enough life span (persistence) in a sequence of nested neighborhoods of the input points. We prove theoretical guarantees when, for a given noisy sample of a graph in the plane, the output contours geometrically approximate the original contours in the unknown graph

Novel perspectives and approaches to video summarization

The increasing volume of videos requires efficient and effective techniques to index and structure videos. Video summarization is such a technique that extracts the essential information from a video, so that tasks such as comprehension by users and video content analysis can be conducted more effectively and efficiently. The research presented in this thesis investigates three novel perspectives of the video summarization problem and provides approaches to such perspectives. Our first perspective is to employ local keypoint to perform keyframe selection. Two criteria, namely Coverage and Redundancy, are introduced to guide the keyframe selection process in order to identify those representing maximum video content and sharing minimum redundancy. To efficiently deal with long videos, a top-down strategy is proposed, which splits the summarization problem to two sub-problems: scene identification and scene summarization. Our second perspective is to formulate the task of video summarization to the problem of sparse dictionary reconstruction. Our method utilizes the true sparse constraint L0 norm, instead of the relaxed constraint L2,1 norm, such that keyframes are directly selected as a sparse dictionary that can reconstruct the video frames. In addition, a Percentage Of Reconstruction (POR) criterion is proposed to intuitively guide users in selecting an appropriate length of the summary. In addition, an L2,0 constrained sparse dictionary selection model is also proposed to further verify the effectiveness of sparse dictionary reconstruction for video summarization. Lastly, we further investigate the multi-modal perspective of multimedia content summarization and enrichment. There are abundant images and videos on the Web, so it is highly desirable to effectively organize such resources for textual content enrichment. With the support of web scale images, our proposed system, namely StoryImaging, is capable of enriching arbitrary textual stories with visual content