The Hough transform estimator

This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose objective is to find the line that ``best'' fits a set of planar points. In particular, we establish strong consistency and rates of convergence, and characterize the limiting distribution of the Hough transform estimator. While the convergence rates are seen to be slower than those found in some standard regression methods, the Hough transform estimator is shown to be more robust as measured by its breakdown point. We next study the Hough transform in the context of the problem of detecting multiple lines. This is addressed via the framework of excess mass functionals and modality testing. Throughout, several numerical examples help illustrate various properties of the estimator. Relations between the Hough transform and more mainstream statistical paradigms and methods are discussed as well.Comment: Published at http://dx.doi.org/10.1214/009053604000000760 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Identifying music documents in a collection of images

Digital libraries and search engines are now well-equipped to find images of documents based on queries. Many images of music scores are now available, often mixed up with textual documents and images. For example, using the Google “images” search feature, a search for “Beethoven” will return a number of scores and manuscripts as well as pictures of the composer. In this paper we report on an investigation into methods to mechanically determine if a particular document is indeed a score, so that the user can specify that only musical scores should be returned. The goal is to find a minimal set of features that can be used as a quick test that will be applied to large numbers of documents. A variety of filters were considered, and two promising ones (run-length ratios and Hough transform) were evaluated. We found that a method based around run-lengths in vertical scans (RL) that out-performs a comparable algorithm using the Hough transform (HT). On a test set of 1030 images, RL achieved recall and precision of 97.8% and 88.4% respectively while HT achieved 97.8% and 73.5%. In terms of processor time, RL was more than five times as fast as HT

Robust approach to object recognition through fuzzy clustering and hough transform based methods

Object detection from two dimensional intensity images as well as three dimensional range images is considered. The emphasis is on the robust detection of shapes such as cylinders, spheres, cones, and planar surfaces, typically found in mechanical and manufacturing engineering applications. Based on the analyses of different HT methods, a novel method, called the Fast Randomized Hough Transform (FRHT) is proposed. The key idea of FRHT is to divide the original image into multiple regions and apply random sampling method to map data points in the image space into the parameter space or feature space, then obtain the parameters of true clusters. This results in the following characteristics, which are highly desirable in any method: high computation speed, low memory requirement, high result resolution and infinite parameter space. This project also considers use of fuzzy clustering techniques, such as Fuzzy C Quadric Shells (FCQS) clustering algorithm but combines the concept of noise prototype to form the Noise FCQS clustering algorithm that is robust against noise. Then a novel integrated clustering algorithm combining the advantages of FRHT and NFCQS methods is proposed. It is shown to be a robust clustering algorithm having the distinct advantages such as: the number of clusters need not be known in advance, the results are initialization independent, the detection accuracy is greatly improved, and the computation speed is very fast. Recent concepts from robust statistics, such as least trimmed squares estimation (LTS), minimum volume ellipsoid estimator (MVE) and the generalized MVE are also utilized to form a new robust algorithm called the generalized LTS for Quadric Surfaces (GLTS-QS) algorithm is developed. The experimental results indicate that the clustering method combining the FRHT and the GLTS-QS can improve clustering performance. Moreover, a new cluster validity method for circular clusters is proposed by considering the distribution of the points on the circular edge. Different methods for the computation of distance of a point from a cluster boundary, a common issue in all the range image clustering algorithms, are also discussed. The performance of all these algorithms is tested using various real and synthetic range and intensity images. The application of the robust clustering methods to the experimental granular flow research is also included

A Specialized Processor for Track Reconstruction at the LHC Crossing Rate

We present the results of an R&D study of a specialized processor capable of precisely reconstructing events with hundreds of charged-particle tracks in pixel detectors at 40 MHz, thus suitable for processing LHC events at the full crossing frequency. For this purpose we design and test a massively parallel pattern-recognition algorithm, inspired by studies of the processing of visual images by the brain as it happens in nature. We find that high-quality tracking in large detectors is possible with sub-$\mu$s latencies when this algorithm is implemented in modern, high-speed, high-bandwidth FPGA devices. This opens a possibility of making track reconstruction happen transparently as part of the detector readout.Comment: Presented by G.Punzi at the conference on "Instrumentation for Colliding Beam Physics" (INSTR14), 24 Feb to 1 Mar 2014, Novosibirsk, Russia. Submitted to JINST proceeding

A Vision-Based Algorithm for UAV State Estimation During Vehicle Recovery

A computer vision-based algorithm for Unmanned Aerial Vehicle state estimation during vehicle recovery is presented. The algorithm is intended to be used to augment or back up Global Positioning System as the primary means of navigation during vehicle recovery for UAVs. The method requires a clearly visible recovery target with markers placed on the corners in addition to known target geometry. The algorithm uses clustering techniques to identify the markers, a Canny Edge detector and a Hough Transform to verify these markers actually lie on the recovery target, an optimizer to match the detected markers with coordinates in three-space, a non-linear transformation and projection solver to observe the position and orientation of the camera, and an Extended Kalman Filter (EKF) to improve the tracking of the state estimate. While it must be acknowledged that the resolution of the test images used is much higher than the resolution of images used in previous algorithms and that the images used to test this algorithm are either synthetic or taken in static conditions, the algorithm presented does give much better state estimates than previously-developed vision systems