Solving optimization tasks based on functions and losses with a topological flavor is a very active and growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and machine learning. However, the approaches proposed in the literature are usually anchored to a specific application and/or topological construction, and do not come with theoretical guarantees. To address this issue, we study the differentiability of a general map associated with the most common topological construction, that is, the persistence map. Building on real analytic geometry arguments, we propose a general framework that allows us to define and compute gradients for persistence-based functions in a very simple way. We also provide a simple, explicit and sufficient condition for convergence of stochastic subgradient methods for such functions. This result encompasses all the constructions and applications of topological optimization in the literature. Finally, we provide associated code, that is easy to handle and to mix with other non-topological methods and constraints, as well as some experiments showcasing the versatility of our approach.

Linear programming relaxations are central to MAP inference in discrete Markov Random Fields. The ability to properly solve the Lagrangian dual is a critical component of such methods. In this paper, we study the benefit of using Newton-type methods to solve the Lagrangian dual of a smooth version of the problem. We investigate their ability to achieve superior convergence behavior and to better handle the ill-conditioned nature of the formulation, as compared to first order methods. We show that it is indeed possible to efficiently apply a trust region Newton method for a broad range of MAP inference problems. In this paper we propose a provably globally efficient framework that includes (i) excellent compromise between computational complexity and precision concerning the Hessian matrix construction, (ii) a damping strategy that aids efficient optimization, (iii) a truncation strategy coupled with a generic pre-conditioner for Conjugate Gradients, (iv) efficient sum-product computation for sparse clique potentials. Results for higher-order Markov Random Fields demonstrate the potential of this approach.

As electronic gadgets become more user friendly, we find natural interaction with the gadgets becoming increasingly popular. Haptic devices have become immensely popular and touch and gesture based interfaces are the logical extension to natural user interaction. We propose to use facial expressions for natural interaction, especially for gadgets like smart phones and tablets where it is more appropriate to capture human faces for user interaction. We present a use-case scenario of an eBook Reader application wherein the user performs certain facial expressions naturally to control the device while using this application. We detect, recognize and interpret these facial expressions for natural interaction with the application. More broadly we want to fit such facial expression based natural interaction to the entire device, not limiting it to a particular application. As we move forward, devices will have to be personalized to comprehend subtle and implicit cues from the user instead of waiting for an explicit input.

We present a robust method to map detected facial Action Units (AUs) to six basic emotions. Automatic AU recognition is prone to errors due to illumination, tracking failures and occlusions. Hence, traditional rule based methods to map AUs to emotions are very sensitive to false positives and misses among the AUs. In our method, a set of chosen AUs are mapped to the six basic emotions using a learned statistical relationship and a suitable matching technique. Relationships between the AUs and emotions are captured as template strings comprising the most discriminative AUs for each emotion. The template strings are computed using a concept called discriminative power. The Longest Common Subsequence (LCS) distance, an approach for approximate string matching, is applied to calculate the closeness of a test string of AUs with the template strings, and hence infer the under lying emotions. LCS is found to be efficient in handling practical issues like erroneous AU detection and helps to reduce false predictions. The proposed method is tested with various databases like CK+, ISL, FACS, JAFFE, MindReading and many real-world video frames. We compare our performance with rule based techniques, and show clear improvement on both benchmark databases and real-world datasets.

For future applications like 3DTV and free view point TV, the video data format is likely to comprise of multiple views plus pre-estimated geometric information such as a depth-map corresponding to each view. It has been well studied that the depth-maps are useful both from compression and rendering perspective. In this paper, we propose two methods which use the concept of depth based 3D warping for efficient multiview video compression. First, we present a method to synthesize virtual view based on 3D warping to enhance inter-view prediction. We analyze similar previous works on view synthesis based inter-view prediction and present comparative results. Next, we propose a novel method that uses 3D warping to improve conventional disparity compensated prediction. Experimental results demonstrate improved coding efficiency with our proposed methods when compared with MVC.

The commercial success and acceptability of 3D technology will critically depend on the overall visual quality of the rendered images. Therefore Depth Image Based Rendering (DIBR) is a crucial component of the 3D system chain. In this paper, we describe a high quality DIBR system for view synthesis. In particular, a procedure is outlined for the processing of the so-called mixed pixels at object boundaries. A Layered Depth Image (LDI) representation of the scene is obtained given an image and corresponding depth map. In the process, all significant mixed pixels in the image are automatically separated into their local foreground and local background. Our results show superior rendering quality, especially at object edges.