Expressing Bayesian Fusion as a Product of Distributions: Application to Randomized Hough Transform

Data fusion is a common issue of mobile robotics, computer assisted medical diagnosis or behavioral control of simulated character for instance. However data sources are often noisy, opinion for experts are not known with absolute precision, and motor commands do not act in the same exact manner on the environment. In these cases, classic logic fails to manage efficiently the fusion process. Confronting different knowledge in an uncertain environment can therefore be adequately formalized in the bayesian framework. Besides, bayesian fusion can be expensive in terms of memory usage and processing time. This paper precisely aims at expressing any bayesian fusion process as a product of probability distributions in order to reduce its complexity. We first study both direct and inverse fusion schemes. We show that contrary to direct models, inverse local models need a specific prior in order to allow the fusion to be computed as a product. We therefore propose to add a consistency variable to each local model and we show that these additional variables allow the use of a product of the local distributions in order to compute the global probability distribution over the fused variable. Finally, we take the example of the Randomized Hough Transform. We rewrite it in the bayesian framework, considering that it is a fusion process to extract lines from couples of dots in a picture. As expected, we can find back the expression of the Randomized Hough Transform from the literature with the appropriate assumptions

Arbitrary shape detection by genetic algorithms.

Wang Tong.Thesis submitted in: June 2004.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 64-69).Abstracts in English and Chinese.ABSTRACT --- p.I摘要 --- p.IVACKNOWLEDGMENTS --- p.VITABLE OF CONTENTS --- p.VIIILIST OF FIGURES --- p.XIIVChapter CHAPTER 1 --- INTRODUCTION --- p.1Chapter 1.1 --- Hough Transform --- p.2Chapter 1.2 --- Template Matching --- p.3Chapter 1.3 --- Genetic Algorithms --- p.4Chapter 1.4 --- Outline of the Thesis --- p.6Chapter CHAPTER 2 --- HOUGH TRANSFORM AND ITS COMMON VARIANTS --- p.7Chapter 2.1 --- Hough Transform --- p.7Chapter 2.1.1 --- What is Hough Transform --- p.7Chapter 2.1.2 --- Parameter Space --- p.7Chapter 2.1.3 --- Accumulator Array --- p.9Chapter 2.2 --- Gradient-based Hough Transform --- p.10Chapter 2.2.1 --- Direction of Gradient --- p.11Chapter 2.2.2 --- Accumulator Array --- p.14Chapter 2.2.3 --- Peaks in the accumulator array --- p.16Chapter 2.2.4 --- Performance of Gradient-based Hough Transform --- p.18Chapter 2.3 --- Generalized Hough Transform (GHT) --- p.19Chapter 2.3.1 --- What Is GHT --- p.19Chapter 2.3.2 --- R-table of GHT --- p.20Chapter 2.3.3 --- GHT Procedure --- p.21Chapter 2.3.4 --- Analysis --- p.24Chapter 2.4 --- Edge Detection --- p.25Chapter 2.4.1 --- Gradient-Based Method --- p.25Chapter 2.4.2 --- Laplacian of Gaussian --- p.29Chapter 2.4.3 --- Canny edge detection --- p.30Chapter CHAPTER 3 --- PROBABILISTIC MODELS --- p.33Chapter 3.1 --- Randomized Hough Transform (RHT) --- p.33Chapter 3.1.1 --- Basics of the RHT --- p.33Chapter 3.1.2 --- RHT algorithm --- p.34Chapter 3.1.3 --- Advantage of RHT --- p.37Chapter 3.2 --- Genetic Model --- p.37Chapter 3.2.1 --- Genetic algorithm mechanism --- p.38Chapter 3.2.2 --- A Genetic Algorithm for Primitive Extraction --- p.39Chapter CHAPTER 4 --- PROPOSED ARBITRARY SHAPE DETECTION --- p.42Chapter 4.1 --- Randomized Generalized Hough Transform --- p.42Chapter 4.1.1 --- R-table properties and the general notion of a shape --- p.42Chapter 4.1.2 --- Using pairs of edges --- p.44Chapter 4.1.3 --- Extend to Arbitrary shapes --- p.46Chapter 4.2 --- A Genetic algorithm with the Hausdorff distance --- p.47Chapter 4.2.1 --- Hausdorff distance --- p.47Chapter 4.2.2 --- Chromosome strings --- p.48Chapter 4.2.3 --- Discussion --- p.51Chapter CHAPTER 5 --- EXPERIMENTAL RESULTS AND COMPARISONS --- p.52Chapter 5.1 --- Primitive extraction --- p.53Chapter 5.2 --- Arbitrary Shape Detection --- p.54Chapter 5.3 --- Summary of the Experimental Results --- p.60Chapter CHAPTER 6 --- CONCLUSIONS --- p.62Chapter 6.1 --- Summary --- p.62Chapter 6.2 --- Future work --- p.63BIBLIOGRAPHY --- p.6

Fast and Robust Normal Estimation for Point Clouds with Sharp Features

Proceedings of the 10th Symposium of on Geometry Processing (SGP 2012), Tallinn, Estonia, July 2012.International audienceThis paper presents a new method for estimating normals on unorganized point clouds that preserves sharp fea- tures. It is based on a robust version of the Randomized Hough Transform (RHT). We consider the filled Hough transform accumulator as an image of the discrete probability distribution of possible normals. The normals we estimate corresponds to the maximum of this distribution. We use a fixed-size accumulator for speed, statistical exploration bounds for robustness, and randomized accumulators to prevent discretization effects. We also propose various sampling strategies to deal with anisotropy, as produced by laser scans due to differences of incidence. Our experiments show that our approach offers an ideal compromise between precision, speed, and robustness: it is at least as precise and noise-resistant as state-of-the-art methods that preserve sharp features, while being almost an order of magnitude faster. Besides, it can handle anisotropy with minor speed and precision losses

An Extension to Hough Transform Based on Gradient Orientation

The Hough transform is one of the most common methods for line detection. In this paper we propose a novel extension of the regular Hough transform. The proposed extension combines the extension of the accumulator space and the local gradient orientation resulting in clutter reduction and yielding more prominent peaks, thus enabling better line identification. We demonstrate benefits in applications such as visual quality inspection and rectangle detection.Comment: Part of the Proceedings of the Croatian Computer Vision Workshop, CCVW 2015, Year

Analisa Kinerja Hough Transform, Randomized Circular Detection, dan Randomized Hough Transform pada Pendeteksian Lingkaran Terhalang dan Ber-noise

Deteksi objek berbentuk lingkaran yang terdapat dalam sebuah citra menjadi hal yang banyak dikembangkan pada saat ini karena dalam kehidupan nyata, banyak objek yang dibentuk dengan dasar lingkaran baik itu objek dalam keadaan sempurna, terhalang oleh benda lain dan mengalami penurunan mutu akibat noise. Dalam penelitin ini, dilakukan perbandingan pendeteksian lingkaran pada benda terhalang dan mengandung noise dengan menggunakan metode Hough Transform (HT), Ranmozid Circle Detection (RCD) dan Randomized Hough Transform (RHT). Perbandingan ketiga metode ini bertujuan untuk mendapatkan metode yang paling sesuai dengan kegunaannya. Penelitian ini dimulai dari akuisisi citra,dan tahap preprocessing . Hasil pre-processing adalah deteksi tepi citra input. Hasil deteksi tepi disimpan untuk dikenali menggunakan metode HT, RCD dan RHT. Untuk menganalisa performansi ketiga metode ini digunakan 135 citra objek lingkaran yang terhalang dan 60 sampel citra yang mengandung noise. Hasil percobaan menunjukkan bahwa dari segi akurasi metode yang lebih akurat mendeteksi adalah HT dan RCD dengan nilai akurasi rata – rata sebesar 80 % pada cita animasi,70,66% dengan metode HT pada citra real. Sedangakan untuk sampel citra ber-noise RCD yang lebih akurat dengan nilai 70% pada citra animasi dan 100% pada citra real. Untuk waktu komputasi metode yang lebih cepat mendeteksi pada sampel citra terhalang adalah RCD dengan nilai kecepatan rata – rata 0,5139 detik pada citra animasi, 0,6420 detik pada citra real, sedangkan pada sampel ber-noise metode RHT yang lebih baik dengan nilai kecepatan rata – rata 1,3829 detik pada citra animasi dan 1,1713 detik pada citra real. Kemudian untuk kebutuhan memori metode yang lebih baik adalah metode RCD dengan nilai memori rata – rata pada sampel citra terhalang adalah 2.902,88 Kb pada citra animasi, 2.906,97 Kb pada citra real, sedangkan untuk sampel citra ber-noise 2.906,97 Kb pada citra animasi, dan 2.938,46 Kb pada citra real Kata kunci: Hough Transform, Randomized Circle Detection, Randomized Hough Transfor

Quantization-free parameter space reduction in ellipse detection

Ellipse modeling and detection is an important task in many computer vision and pattern recognition applications. In this thesis, four Hough-based transform algorithms have been carefully selected, studied and analyzed. These techniques include the Standard Hough Transform, Probabilistic Hough Transform, Randomized Hough Transform and Directional Information for Parameter Space Decomposition. The four algorithms are analyzed and compared against each other in this study using synthetic ellipses. Objects such as noise have been introduced to distract ellipse detection in some of the synthetic ellipse images. To complete the analysis, real world images were used to test each algorithm resulting in the proposal of a new algorithm. The proposed algorithm uses the strengths from each of the analyzed algorithms. This new algorithm uses the same approach as the Directional Information for Parameter Space Decomposition to determine the ellipse center. However, in the process of collecting votes for the ellipse center, pairs of unique edge points voted for the center are also kept in an array. A minimum of two pairs of edge points are required to determine the ellipse. This significantly reduces the usual five dimensional array requirement needed in the Standard Hough Transform. We present results of the experiments with synthetic images demonstrating that the proposed method is more effective and robust to noise. Real world applications on complex real world images are also performed successfully in the experiment