Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms

We consider the RMS distance (sum of squared distances between pairs of points) under translation between two point sets in the plane, in two different setups. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision of the plane and derive improved bounds on its complexity. These results lead to the best known algorithm for finding a translation for which the partial-matching RMS distance between the point sets is minimized. In addition, we show how to compute a local minimum of the partial-matching RMS distance under translation, in polynomial time. In the Hausdorff setup, each point is paired to its nearest neighbor in the other set. We develop algorithms for finding a local minimum of the Hausdorff RMS distance in nearly linear time on the line, and in nearly quadratic time in the plane. These improve substantially the worst-case behavior of the popular ICP heuristics for solving this problem.Comment: 31 pages, 6 figure

Minimum Partial-Matching and Hausdorff RMS-Distance under Translation: Combinatorics and Algorithms

We consider the RMS-distance (sum of squared distances between pairs of points) under translation between two point sets in the plane. In the Hausdorff setup, each point is paired to its nearest neighbor in the other set. We develop algorithms for finding a local minimum in near-linear time on the line, and in nearly quadratic time in the plane. These improve substantially the worst-case behavior of the popular ICP heuristics for solving this problem. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision of the plane and derive improved bounds on its complexity. In addition, we show how to compute a local minimum of the partial-matching RMS-distance under translation, in polynomial time

Partial-Matching RMS Distance Under Translation: Combinatorics and Algorithms

We consider the problem of minimizing the RMS distance (sum of squared distances between pairs of points) under translation between two point sets A and B, in the plane, with (Formula presented.), in the partial-matching setup, in which each point in B is matched to a distinct point in A. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision (Formula presented.) of the plane and derive improved bounds on its complexity. Specifically, we show that this complexity is (Formula presented.), so it is only quadratic in |A|. These results lead to the best known algorithm for finding a translation for which the partial-matching RMS distance between the point sets is minimized. In addition, we show how to compute a local minimum of the partial-matching RMS distance under translation, in polynomial time. © 2017 Springer Science+Business Media New Yor

A new asymmetrical corner detector(ACD) for a semi-automatic image co-registration scheme

Co-registration of multi-sensor and multi-temporal images is essential for remote sensing applications. In the image co-registration process, automatic Ground Control Points (GCPs) selection is a key technical issue and the accuracy of GCPs localization largely accounts for the final image co-registration accuracy. In this thesis, a novel Asymmetrical Corner Detector (ACD) algorithm based on auto-correlation is presented and a semi-automatic image co-registration scheme is proposed. The ACD is designed with the consideration of the fact that asymmetrical corner points are the most common reality in remotely sensed imagery data. The ACD selects points more favourable to asymmetrical points rather than symmetrical points to avoid incorrect selection of flat points which are often highly symmetrical. The experimental results using images taken by different sensors indicate that the ACD has obtained excellent performance in terms of point localization and computation efficiency. It is more capable of selecting high quality GCPs than some well established corner detectors favourable to symmetrical corner points such as the Harris Corner Detector (Harris and Stephens, 1988). A semi-automatic image co-registration scheme is then proposed, which employs the ACD algorithm to extract evenly distributed GCPs across the overlapped area in the reference image. The scheme uses three manually selected pairs of GCPs to determine the initial transformation model and the overlapped area. Grid-control and nonmaximum suppression methods are used to secure the high quality and spread distribution of GCPs selected. It also involves the FNCC (fast normalised crosscorrelation) algorithm (Lewis, 1995) to refine the corresponding point locations in the input image and thus the GCPs are semi-automatically selected to proceed to the polynomial fitting image rectification. The performance of the proposed coregistration scheme has been demonstrated by registering multi-temporal, multi-sensor and multi-resolution images taken by Landsat TM, ETM+ and SPOT sensors. Experimental results show that consistent high registration accuracy of less than 0.7 pixels RMSE has been achieved. Keywords: Asymmetrical corner points, image co-registration, AC

Visual odometry: feature based tracking and velocity estimation based on ground looking camera

The computer vision field has close relation with autonomous robotics which is in use for several purposes which include mobile robot vision tasks, robot navigation, motion trajectory, object detection and tracking and security surveillance tasks. There are many techniques available which are being used for completing these tasks but many of them lead to problems like low resolution, limited applicability and high capital investment. This thesis examines the way in which we could achieve results within some tolerance level of accuracy and low cost. Visual odometery is one of the main objectives of this thesis which is achieved with simple and practical method. The algorithm is developed to estimate the velocity using a corner detection technique based on ground looking camera. The thesis is divided into three main parts. In the first part of the thesis, literature review and previous work done in the relevant field is explained. The theoretical background of the topic is also described in the first part of the thesis. Second part of the thesis demonstrates the development of the algorithm, pre and post processing and implementation of the algorithm. Last part of the thesis describes the different test environments where the developed algorithm is implemented. The test environments are further classified into two main categories. Conclusions, results, problems faced during the whole process and future tasks are also included in the last part of the thesis. The study indicates that, selection of the right pre-processing parameters can enhance the results quality. At the same time by providing the appropriate illumination for the camera system can also increase the efficiency of the outcome. This research and developed algorithm has the potential to be used for further implementation at commercial level by changing some necessary parameters in the algorithm and implementation. This research could be more useful by implementing addressed future tasks in Section 5.3.2, in order to achieve higher efficiency in the results. Implementation of all necessary parameters explained in this thesis and by considering future tasks will make this research more effective and beneficial for the business

Embedded landmark acquisition system for visual slam using star identification based stereo correspondence descriptor

Orientador : Prof. Dr. Eduardo TodtDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 13/04/2015Inclui referênciasResumo: O uso de câmeras como sensores principais em Localização e Mapeamento Simultâneos (Simultaneous Localization and Mapping), o que é denominado SLAM Visual (Visual SLAM), tem crescido recentemente devido à queda nos preços das câmeras. Ao mesmo tempo em que imagens trazem informações mais ricas do que outros sensores típicos empregados em aplicações SLAM, como lasers e sonares, há um custo adicional de processamento significativo quando elas são utilizadas. A informação de profundidade adicional proveniente de configurações estéreo de câmeras às fazem mais interessantes para aplicações SLAM. Nesta abordagem em especial, grande parte do custo de processamento adicional vem da extração de pontos únicos ou pedaços em ambas as imagens em estéreo e da solução do problema de correspondência entre eles. Com posse dessa informação, a disparidade horizontal entre o par de imagens pode ser utilizada para recuperar a informação de profundidade. Esse trabalho explora a utilização de uma plataforma embarcada do tipo system-ona- chip (SoC) que integra um processador ARM multinúcleo com lógica FPGA como um módulo de processamento para visão estéreo. O detector de cantos Harris e Stephens (Harris & Stephens, 1988) é usado para encontrar pontos de interesse (Points of Interest, POIs) em imagens estéreo em um coprocessador soft sintetizado no FPGA para acelerar a extração de características e livrar o processador principal deste processo altamente paralelizável. As tarefas restantes tais como correção das imagens pela calibração de câmeras, encontrar um descritor único para as características detectadas e a correspondência entre os POIs no par de imagens estéreo são solucionadas em software executando no processador principal. A arquitetura proposta para o coprocessador permite que a tarefa de extração de cantos seja executada em aproximadamente metade do tempo necessário pelo processador principal sem auxílio algum. Após encontrar os POIs, para cada um dos pontos um descritor único é necessário para que seja possível encontrar o POI correspondente na outra imagem. Esse trabalho também propõe um descritor inovador que considera o relacionamento espacial bidimensional global entre os pontos detectados para descrevê-los individualmente. Para cada imagem, cada ponto da nuvem de pontos detectada pelo algoritmo de Harris e Stephens é descrito considerando-se apenas as posições relativas entre ele e seus vizinhos. Quando somente a posição é considerada, um padrão de céu estrelado noturno é formado pelos POIs. Com o padrão de POIs sendo considerado como estrelas, descritores já utilizados em problemas de identificação de estrelas podem ser reaplicados para identificar unicamente POIs. Um protótipo do descritor baseado do algoritmo de grade de Padgett e KreutzDelgado (Padgett & KreutzDelgado, 1997) é escrito e seus resultados comparados com os descritores normalmente utilizados para este propósito, mostrando que a informação espacial bidimensional pode ser utilizada por si só para resolver o problema de correspondência. O número de correspondências úteis é comparável ao atingido com o SIFT, o descritor com melhor desempenho neste quesito, enquanto a velocidade foi superior ao BRIEF, o descritor mais rápido utilizado na comparação, na plataforma ARM, com um speedup de 1,64 e 1,40 nas bases de dados dos testes. Palavras-chave: Harris; FPGA; SLAM; Hardware Reconfigurável; VHDL; Processamento de Imagem; Visão Estéreo; Computer Vision; Arquitetura Híbrida; Sistemas Embarcados; Pontos de Interesse; Keypoints; Correspondência; Correspondência Estéreo; Identificação de Estrelas; Descrição de Características; Percepção de Profundidade.Abstract: The use of cameras as the main sensors in Simultaneous Localization and Mapping, what is called Visual SLAM, has risen recently due to the fall in camera prices. While images bring richer information than other typical SLAM sensors, such as lasers and sonars, there is significant extra processing cost when they are used. The extra depth information available from stereo camera setups makes them preferable for SLAM applications. In this particular approach, great part of the added processing cost comes from extracting unique points or image patches in both stereo images and solving the correspondence problem between them. With this information, the horizontal disparity between the pair can be used to retrieve depth information. This work explores the use of an embedded system-on-a-chip (SoC) platform that integrates a multicore ARM processor with FPGA fabric as a stereo vision processing module. The Harris and Stephens corner detector (Harris & Stephens, 1988) is used to find Point of Interests (POIs) in stereo images in a hardware soft co-processor synthesized in the FPGA to speed up feature extraction and relieve this highly parallelizable process from the main embedded processor. Remaining tasks such as image correction from camera calibration, finding unique descriptor for the detected features and the correspondence between POIs in the stereo pair are solved in software running on the main processor. The proposed architecture for the co-processor enabled the corner extraction task to be performed in about half the time taken by the main processor without aid. After finding the POIs, for each point a unique descriptor is needed for finding the correspondent POI in the other image. This work also proposes an innovative descriptor that considers a global two-dimensional spatial relationship between the detected points to describe them individually. In each image, every point in the cloud of points detected by the Harris and Stephens algorithm is described by considering only the relative position between it and its neighbors. When position alone is considered, a starry night pattern is formed by the POIs. With the POI pattern being considered as stars, the descriptors already used in star identification problems can be reapplied to uniquely identify POIs. A prototype of the descriptor based on the Padgett and KreutzDelgado's grid algorithm (Padgett & KreutzDelgado, 1997) is written and the results compared with common descriptors used for this purpose, showing that two-dimensional spatial information alone can be used to solve the correspondence problem. The number of useful matches was comparable to what was obtained with SIFT, the best performing descriptor in this matter, while the speed was superior to BRIEF, the fastest descriptor used in the comparison, on the ARM platform, with a speedup of 1.64 and 1.40 on the tested datasets. Keywords: Harris; FPGA; SLAM; Reconfigurable Hardware; VHDL; Image Processing; Stereo Vision; Computer Vision; Hybrid Architecture; Embedded Systems; Point Of Interest; Keypoints; Matching; Stereo Correspondence; Star Identification; Feature Description; Depth Perception

Accurate 3D shape and displacement measurement using a scanning electron microscope

With the current development of nano-technology, there exists an increasing demand for three-dimensional shape and deformation measurements at this reduced-length scale in the field of materials research. Images acquired by \ud Scanning Electron Microscope (SEM) systems coupled with analysis by Digital Image Correlation (DIC) is an interesting combination for development of a high magnification measurement system. However, a SEM is designed for visualization, not for metrological studies, and the application of DIC to the micro- or nano-scale with such a system faces the challenges of calibrating the imaging system and correcting the spatially-varying and \ud time-varying distortions in order to obtain accurate measurements. Moreover, the SEM provides only a single sensor and recovering 3D information is not possible with the classical stereo-vision approach. But the specimen being mounted on the mobile SEM stage, images can be acquired from multiple viewpoints and 3D reconstruction is possible using the principle of videogrammetry for recovering the unknown rigid-body motions undergone by \ud the specimen.\ud The dissertation emphasizes the new calibration methodology that has been developed because it is a major contribution for the accuracy of 3D shape and deformation measurements at reduced-length scale. It proves that, unlike previous works, image drift and distortion must be taken into account if accurate measurements are to be made with such a system. Necessary background and required theoretical knowledge for the 3D shape measurement using videogrammetry and for in-plane and out-of-plane deformation measurement are presented in details as well. In order to validate our work and demonstrate in particular the obtained measurement accuracy, experimental results resulting from different applications are presented throughout the different chapters. At last, a software gathering different computer vision applications has been developed.\ud Avec le développement actuel des nano-technologies, la demande en matière d'étude du comportement des matériaux à des échelles micro ou nanoscopique ne cesse d'augmenter. Pour la mesure de forme ou de déformations tridimensionnelles à ces échelles de grandeur,l'acquisition d'images à partir d'un Microscope électronique à Balayage (MEB) couplée à l'analyse par corrélation d'images numériques s'est avérée une technique intéressante. \ud Cependant, un MEB est un outil conçu essentiellement pour de la visualisation et son utilisation pour des mesures tridimensionnelles précises pose un certain nombre de difficultés comme par exemple le calibrage du système et la \ud correction des fortes distorsions (spatiales et temporelles) présentes dans les images. De plus, le MEB ne possède qu'un seul capteur et les informations tridimensionnelles souhaitées ne peuvent pas être obtenues par une approche classique de type stéréovision. Cependant, l'échantillon à analyser étant monté sur un support orientable, des images peuvent être acquises sous différents points de vue, ce qui permet une reconstruction tridimensionnelle en utilisant le principe de vidéogrammétrie pour retrouver à partir des seules images les mouvements inconnus du porte-échantillon.\ud La thèse met l'accent sur la nouvelle technique de calibrage et de correction des distorsions développée car c'est une contribution majeure pour la précision de la mesure de forme et de déformations 3D aux échelles de \ud grandeur étudiées. Elle prouve que, contrairement aux travaux précédents, la prise en compte de la dérive temporelle et des distorsions spatiales d'images \ud est indispensable pour obtenir une précision de mesure suffisante. Les principes permettant la mesure de forme par vidéogrammétrie et le calcul de déformations 2D et 3D sont aussi présentés en détails. Enfin, et dans le but de valider nos travaux et démontrer en particulier la précision de mesure obtenue, des résultats expérimentaux issus de différentes applications sont présentés.\ud \ud \u

Efficient Algorithms for Robust Estimation

One of the most commonly encountered tasks in computer vision is the estimation of model parameters from image measurements. This scenario arises in a variety of applications -- for instance, in the estimation of geometric entities, such as camera pose parameters, from feature matches between images. The main challenge in this task is to handle the problem of outliers -- in other words, data points that do not conform to the model being estimated. It is well known that if these outliers are not properly accounted for, even a single outlier in the data can result in arbitrarily bad model estimates. Due to the widespread prevalence of problems of this nature, the field of robust estimation has been well studied over the years, both in the statistics community as well as in computer vision, leading to the development of popular algorithms like Random Sample Consensus (RANSAC). While recent years have seen exciting advances in this area, a number of important issues still remain open. In this dissertation, we aim to address some of these challenges. The main goal of this dissertation is to advance the state of the art in robust estimation techniques by developing algorithms capable of efficiently and accurately delivering model parameter estimates in the face of noise and outliers. To this end, the first contribution of this work is in the development of a coherent framework for the analysis of RANSAC-based robust estimators, which consolidates various improvements made over the years. In turn, this analysis leads naturally to the development of new techniques that combine the strengths of existing methods, and yields high-performance robust estimation algorithms, including for real-time applications. A second contribution of this dissertation is the development of an algorithm that explicitly characterizes the effects of estimation uncertainty in RANSAC. This uncertainty arises from small-scale measurement noise that affects the data points, and consequently, impacts the accuracy of model parameters. We show that knowledge of this measurement noise can be leveraged to develop an inlier classification scheme that is dependent on the model uncertainty, as opposed to a fixed inlier threshold, as in RANSAC. This has the advantage that, given a model with associated uncertainty, we can immediately identify a set of points that support this solution, which in turn leads to an improvement in computational efficiency. Finally, we have also developed an approach to addresses the issue of the inlier threshold, which is a user-supplied parameter that can vary depending on the estimation problem and the data being processed. Our technique is based on the intuition that the residual errors for good models are in some way consistent with each other, while bad models do not exhibit this consistency. In other words, looking at the relationship between \\subsets of models can reveal useful information about the validity of the models themselves. We show that it is possible to efficiently identify this consistent behaviour by exploiting residual ordering information coupled with simple non-parametric statistical tests, which leads to an effective algorithm for threshold-free robust estimation.Doctor of Philosoph