A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima

Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.

Low rank subspace clustering (LRSC)

We consider the problem of fitting a union of subspaces to a collection of data points drawn from one or more subspaces and corrupted by noise and/or gross errors. We pose this problem as a non-convex optimization problem, where the goal is to decompose the corrupted data matrix as the sum of a clean and self-expressive dictionary plus a matrix of noise and/or gross errors. By self-expressive we mean a dictionary whose atoms can be expressed as linear combinations of themselves with low-rank coefficients. In the case of noisy data, our key contribution is to show that this non-convex matrix decomposition problem can be solved in closed form from the SVD of the noisy data matrix. The solution involves a novel polynomial thresholding operator on the singular values of the data matrix, which requires minimal shrinkage. For one subspace, a particular case of our framework leads to classical PCA, which requires no shrinkage. For multiple subspaces, the low-rank coefficients obtained by our framework can be used to construct a data affinity matrix from which the clustering of the data according to the subspaces can be obtained by spectral clustering. In the case of data corrupted by gross errors, we solve the problem using an alternating minimization approach, which combines our polynomial thresholding operator with the more traditional shrinkage-thresholding operator. Experiments on motion segmentation and face clustering show that our framework performs on par with state-of-the-art techniques at a reduced computational cost.

Parsing for agile modeling

In order to analyze software systems, it is necessary to model them. Static software models are commonly imported by parsing source code and related data. Unfortunately, building custom parsers for most programming languages is a non-trivial endeavour. This poses a major bottleneck for analyzing software systems programmed in languages for which importers do not already exist. Luckily, initial software models do not require detailed parsers, so it is possible to start analysis with a coarse-grained importer, which is then gradually refined. In this paper we propose an approach to "agile modeling" that exploits island grammars to extract initial coarse-grained models, parser combinators to enable gradual refinement of model importers, and various heuristics to recognize language structure, keywords and other language artifacts.

Behind the curtains of privacy calculus on social networking sites: the study of Germany and the USA

As social networking sites (SNSs) become increasingly global, the issues of cultural differences in participation patterns become acute. However, current research offers only limited insights into the role of culture behind SNS usage. Aiming to fill this gap, this study adopts a ‘privacy calculus’ perspective to study the differences between German and American SNS users. Results of structural equation modeling and multi-group analysis reveal distinct variability in the cognitive patterns of American and German subjects. We contribute to the theory by rejecting the universal nature of privacy-calculus processes. From a practical standpoint, our results signal that SNS providers cannot rely on the “proven” means in ensuring user participation when crossing geographic boundaries. When financial means are limited, SNS providers should direct their investments into enhancing platform enjoyment and granting users with more control and, paradoxically, lobbying for more legalistic safeguards of user privacy.