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This paper presents a novel formulation for the popular factorisation based solution for Structure from Motion. Since our measurement matrices are populated with incomplete and inaccurate data, SVD based total least squares solution are less than appropriate. Instead, we approach the problem as a non-linear unconstrained minimisation problem on the product manifold of the Special Euclidean Group (SE3). The restriction of the domain of optimisation to the SE3 product manifold not only implies that each intermediate solution is a plausible object motion, but also ensures better intrinsic stability for the minimisation algorithm. We compare our method with existing state of art, and show that our algorithm exhibits superior performance.

It is useful to have a small set of representative images from a database of thousands of images to summarize its content. There are two key aspects of such image summaries: how to generate them and how to present them. We address both issues. We extend the idea of image saliency to databases and introduce the notion of database saliency. We argue that in image databases, there are certain images that are more uncommon or salient than others and therefore are more interesting. We compute the database saliency value of an image as its total distance from all the pre-defined cluster centers of the database. We demonstrate the use of database saliency in two visualization applications: creating image collages and mosaics using automatically chosen salient images.

Computer vision applications have come to rely increasingly on superpixels in recent years, but it is not always clear what constitutes a good superpixel algorithm. In an effort to understand the benefits and drawbacks of existing methods, we empirically compare five state-of-the-art superpixel algorithms for their ability to adhere to image boundaries, speed, memory efficiency, and their impact on segmentation performance. We then introduce a new superpixel algorithm, simple linear iterative clustering (SLIC), which adapts a k-means clustering approach to efficiently generate superpixels. Despite its simplicity, SLIC adheres to boundaries as well as or better than previous methods. At the same time, it is faster and more memory efficient, improves segmentation performance, and is straightforward to extend to supervoxel generation.

The currently best performing state-of-the-art saliency detection algorithms incorporate heuristic functions to evaluate saliency. They require parameter tuning, and the relationship between the parameter value and visual saliency is often not well understood. Instead of using parametric methods we follow a ma- chine learning approach, which is parameter free, to estimate saliency. Our method learns data-driven saliency-estimation functions and exploits the contributions of visual properties on saliency. First, we over-segment the image into superpixels and iteratively connect them to form hierarchical image segments. Second, from these segments, we extract biologically- plausible visual features. Finally, we use regression trees to learn the relationship between the feature values and visual saliency. We show that our algorithm outperforms the most recent state-of-the-art methods on three public databases.

It has been shown that the 3D shape of a deformable surface in an image can be recovered by establishing correspondences between that image and a reference one in which the shape is known. These matches can then be used to set-up a convex optimization problem in terms of the shape parameters, which is easily solved. However, in many cases, the correspondences are hard to establish reliably. In this paper, we show that we can solve simultaneously for both 3D shape and correspondences, thereby using 3D shape constraints to guide the image matching and increasing robustness, for example when the textures are repetitive. This involves solving a mixed integer quadratic problem. While optimizing this problem is NP-hard in general, we show that its solution can nevertheless be approximated effectively by a branch-and-bound algorithm.