Information-based mapping algorithms are critical to robot exploration tasks in several applications ranging from disaster response to space exploration. Unfortunately, most existing information-based mapping algorithms are plagued by the computational difficulty of evaluating the Shannon mutual information between potential future sensor measurements and the map. This has lead researchers to develop approximate methods, such as Cauchy-Schwarz Quadratic Mutual Information (CSQMI). In this paper, we propose a new algorithm, called Fast Shannon Mutual Information (FSMI), which is significantly faster than existing methods at computing the exact Shannon mutual information. The key insight behind FSMI is recognizing that the integral over the sensor beam can be evaluated analytically, removing an expensive numerical integration. In addition, we provide a number of approximation techniques for FSMI, which significantly improve computation time. Equipped with these approximation techniques, the FSMI algorithm is more than three orders of magnitude faster than the existing computation for Shannon mutual information; it also outperforms the CSQMI algorithm significantly, being roughly twice as fast, in our experiments.

This paper proposes a method called rotate intra block copy, which extends the intra block copy technique by making the block matching process invariant to rotation. HEVC intra prediction plus rotate intra block copy gives an average of 20% reduction in residual energy (i.e. prediction error) compared to HEVC intra prediction plus intra block copy. As the motion vector correlation in rotate intra block copy is different from the intra block copy, a new method of motion vector coding is presented. The impact of angular resolution on residual energy reduction is also evaluated. In a full codec pipeline, this reduction in residual energy translates into a coding gain in BD-rate of 3.4% over HEVC intra prediction plus intra block copy for both screen content and camera-captured gray scale images.

This letter examines the problem of robust subspace discovery from input data samples (instances) in the presence of overwhelming outliers and corruptions. A typical example is the case where we are given a set of images; each image contains, for example, a face at an unknown location of an unknown size; our goal is to identify or detect the face in the image and simultaneously learn its model. We employ a simple generative subspace model and propose a new formulation to simultaneously infer the label information and learn the model using low-rank optimization. Solving this problem enables us to simultaneously identify the ownership of instances to the subspace and learn the corresponding subspace model. We give an efficient and effective algorithm based on the alternating direction method of multipliers and provide extensive simulations and experiments to verify the effectiveness of our method. The proposed scheme can also be used to tackle many related high-dimensional combinatorial selection problems.

We present a simple, accurate, and flexible method to calibrate intrinsic parameters of a camera together with (possibly significant) lens distortion. This new method can work under a wide range of practical scenarios: using multiple images of a known pattern, multiple images of an unknown pattern, single or multiple image(s) of multiple patterns, etc. Moreover, this new method does not rely on extracting any low-level features such as corners or edges. It can tolerate considerably large lens distortion, noise, error, illumination and viewpoint change, and still obtain accurate estimation of the camera parameters. The new method leverages on the recent breakthroughs in powerful high-dimensional convex optimization tools, especially those for matrix rank minimization and sparse signal recovery. We will show how the camera calibration problem can be formulated as an important extension to principal component pursuit, and solved by similar techniques. We characterize to exactly what extent the parameters can be recovered in case of ambiguity. We verify the efficacy and accuracy of the proposed algorithm with extensive experiments on real images.

In this paper, we show how to reconstruct both 3D shape and 2D texture of a class of surfaces from a single perspective image. We consider the so-called the generalized cylindrical surfaces that are wrapped with low-rank textures. They can be used to model most curved building facades in urban areas or deformed book pages scanned for text recognition. Our method leverages on the recent new techniques for low-rank matrix recovery and sparse error correction and it generalizes existing techniques from planar surfaces to a much larger class of important 3D surfaces. As we will show with extensive simulations and experiments, the proposed algorithm can precisely rectify deformation of textures caused by both perspective projection and surface shape. It works for a wide range of symmetric or regular textures that are ubiquitous in images of urban environments, objects, or texts, and it is very robust to sparse occlusion, noise, and saturation.

Low-dimensional topic models have been proven very useful for modeling a large corpus of documents that share a relatively small number of topics. Dimensionality reduction tools such as Principal Component Analysis or Latent Semantic Indexing (LSI) have been widely adopted for document modeling, analysis, and retrieval. In this paper, we contend that a more pertinent model for a document corpus as the combination of an (approximately) low-dimensional topic model for the corpus and a sparse model for the keywords of individual documents. For such a joint topic-document model, LSI or PCA is no longer appropriate to analyze the corpus data. We hence introduce a powerful new tool called Principal Component Pursuit that can effectively decompose the low-dimensional and the sparse components of such corpus data. We give empirical results on data synthesized with a Latent Dirichlet Allocation (LDA) mode to validate the new model. We then show that for real document data analysis, the new tool significantly reduces the perplexity and improves retrieval performance compared to classical baselines.