Automatic Detection of Calibration Grids in Time-of-Flight Images

It is convenient to calibrate time-of-flight cameras by established methods, using images of a chequerboard pattern. The low resolution of the amplitude image, however, makes it difficult to detect the board reliably. Heuristic detection methods, based on connected image-components, perform very poorly on this data. An alternative, geometrically-principled method is introduced here, based on the Hough transform. The projection of a chequerboard is represented by two pencils of lines, which are identified as oriented clusters in the gradient-data of the image. A projective Hough transform is applied to each of the two clusters, in axis-aligned coordinates. The range of each transform is properly bounded, because the corresponding gradient vectors are approximately parallel. Each of the two transforms contains a series of collinear peaks; one for every line in the given pencil. This pattern is easily detected, by sweeping a dual line through the transform. The proposed Hough-based method is compared to the standard OpenCV detection routine, by application to several hundred time-of-flight images. It is shown that the new method detects significantly more calibration boards, over a greater variety of poses, without any overall loss of accuracy. This conclusion is based on an analysis of both geometric and photometric error.Comment: 11 pages, 11 figures, 1 tabl

Connectivity-Enforcing Hough Transform for the Robust Extraction of Line Segments

Global voting schemes based on the Hough transform (HT) have been widely used to robustly detect lines in images. However, since the votes do not take line connectivity into account, these methods do not deal well with cluttered images. In opposition, the so-called local methods enforce connectivity but lack robustness to deal with challenging situations that occur in many realistic scenarios, e.g., when line segments cross or when long segments are corrupted. In this paper, we address the critical limitations of the HT as a line segment extractor by incorporating connectivity in the voting process. This is done by only accounting for the contributions of edge points lying in increasingly larger neighborhoods and whose position and directional content agree with potential line segments. As a result, our method, which we call STRAIGHT (Segment exTRAction by connectivity-enforcInG HT), extracts the longest connected segments in each location of the image, thus also integrating into the HT voting process the usually separate step of individual segment extraction. The usage of the Hough space mapping and a corresponding hierarchical implementation make our approach computationally feasible. We present experiments that illustrate, with synthetic and real images, how STRAIGHT succeeds in extracting complete segments in several situations where current methods fail.Comment: Submitted for publicatio

Progressive Probabilistic Hough Transform for line detection

We present a novel Hough Transform algorithm referred to as Progressive Probabilistic Hough Transform (PPHT). Unlike the Probabilistic HT where Standard HT is performed on a pre-selected fraction of input points, PPHT minimises the amount of computation needed to detect lines by exploiting the difference an the fraction of votes needed to detect reliably lines with different numbers of supporting points. The fraction of points used for voting need not be specified ad hoc or using a priori knowledge, as in the probabilistic HT; it is a function of the inherent complexity of the input data. The algorithm is ideally suited for real-time applications with a fixed amount of available processing time, since voting and line detection is interleaved. The most salient features are likely to be detected first. Experiments show that in many circumstances PPHT has advantages over the Standard HT

Automated Generation of Geometric Theorems from Images of Diagrams

We propose an approach to generate geometric theorems from electronic images of diagrams automatically. The approach makes use of techniques of Hough transform to recognize geometric objects and their labels and of numeric verification to mine basic geometric relations. Candidate propositions are generated from the retrieved information by using six strategies and geometric theorems are obtained from the candidates via algebraic computation. Experiments with a preliminary implementation illustrate the effectiveness and efficiency of the proposed approach for generating nontrivial theorems from images of diagrams. This work demonstrates the feasibility of automated discovery of profound geometric knowledge from simple image data and has potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial Intelligence (special issue on Geometric Reasoning

Unsupervised Object Discovery and Localization in the Wild: Part-based Matching with Bottom-up Region Proposals

This paper addresses unsupervised discovery and localization of dominant objects from a noisy image collection with multiple object classes. The setting of this problem is fully unsupervised, without even image-level annotations or any assumption of a single dominant class. This is far more general than typical colocalization, cosegmentation, or weakly-supervised localization tasks. We tackle the discovery and localization problem using a part-based region matching approach: We use off-the-shelf region proposals to form a set of candidate bounding boxes for objects and object parts. These regions are efficiently matched across images using a probabilistic Hough transform that evaluates the confidence for each candidate correspondence considering both appearance and spatial consistency. Dominant objects are discovered and localized by comparing the scores of candidate regions and selecting those that stand out over other regions containing them. Extensive experimental evaluations on standard benchmarks demonstrate that the proposed approach significantly outperforms the current state of the art in colocalization, and achieves robust object discovery in challenging mixed-class datasets.Comment: CVPR 201