Vanishing of cohomology over Cohen--Macaulay rings

A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings - colloquially called AC rings - that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen--Macaulay rings. In particular, we show that the AC property is preserved by standard procedures in local algebra. Our results also yield new examples of Cohen-Macaulay AC rings.Comment: Updated references. Final version to appear in Manuscripta Math.; 9 p

Ascent Properties of Auslander Categories

Let R be a homomorphic image of a Gorenstein local ring. Recent work has shown that there is a bridge between Auslander categories and modules of finite Gorenstein homological dimensions over R. We use Gorenstein dimensions to prove new results about Auslander categories and vice versa. For example, we establish base change relations between the Auslander categories of the source and target rings in a homomorphism R -> S of finite flat dimension.Comment: Minor corrections; example added; 30 pp. To appear in Canad. J. Math. Also available from authors' homepages http://www.math.unl.edu/~lchristensen3/publications.html and http://home.imf.au.dk/holm/publications.htm

Occlusion-Aware Object Localization, Segmentation and Pose Estimation

We present a learning approach for localization and segmentation of objects in an image in a manner that is robust to partial occlusion. Our algorithm produces a bounding box around the full extent of the object and labels pixels in the interior that belong to the object. Like existing segmentation aware detection approaches, we learn an appearance model of the object and consider regions that do not fit this model as potential occlusions. However, in addition to the established use of pairwise potentials for encouraging local consistency, we use higher order potentials which capture information at the level of im- age segments. We also propose an efficient loss function that targets both localization and segmentation performance. Our algorithm achieves 13.52% segmentation error and 0.81 area under the false-positive per image vs. recall curve on average over the challenging CMU Kitchen Occlusion Dataset. This is a 42.44% decrease in segmentation error and a 16.13% increase in localization performance compared to the state-of-the-art. Finally, we show that the visibility labelling produced by our algorithm can make full 3D pose estimation from a single image robust to occlusion.Comment: British Machine Vision Conference 2015 (poster

GASP : Geometric Association with Surface Patches

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel) associations, requiring just range information. Our approach involves decomposition of a view into regularized surface patches. We represent them as sequences expressing geometry invariantly over their superpixel neighborhoods, as uniquely consistent partial orderings. We match these representations through an optimal sequence comparison metric based on the Damerau-Levenshtein distance - enabling robust association with quadratic complexity (in contrast to hitherto employed joint matching formulations which are NP-complete). The approach is able to perform under wide baselines, heavy rotations, partial overlaps, significant occlusions and sensor noise. The technique does not require any priors -- motion or otherwise, and does not make restrictive assumptions on scene structure and sensor movement. It does not require appearance -- is hence more widely applicable than appearance reliant methods, and invulnerable to related ambiguities such as textureless or aliased content. We present promising qualitative and quantitative results under diverse settings, along with comparatives with popular approaches based on range as well as RGB-D data.Comment: International Conference on 3D Vision, 201

Using Students’ Screencasts as Alternative to Written Submissions

In this paper, we report our experiences on using student produced screencasts as a medium for students to explain and provide overview of their solution to advanced design and programming exercises. In our context, the screencasts have replaced written reports as submissions, and we report both on students' perception on work effort and effectiveness of screencasts as well as teaching assistants' experiences in assessing and marking the screencasts. Our main conclusions are that screencasted submissions is an important tool in the teacher's toolbox for some categories of learning tasks, but there are a number of best practices to follow to gain the full benefits of the approach