Pedestrian Detection Algorithms using Shearlets

In this thesis, we investigate the applicability of the shearlet transform for the task of pedestrian detection. Due to the usage of in several emerging technologies, such as automated or autonomous vehicles, pedestrian detection has evolved into a key topic of research in the last decade. In this time period, a wealth of different algorithms has been developed. According to the current results on the Caltech Pedestrian Detection Benchmark the algorithms can be divided into two categories. First, application of hand-crafted image features and of a classifier trained on these features. Second, methods using Convolutional Neural Networks in which features are learned during the training phase. It is studied how both of these types of procedures can be further improved by the incorporation of shearlets, a framework for image analysis which has a comprehensive theoretical basis

Image Feature Information Extraction for Interest Point Detection: A Comprehensive Review

Interest point detection is one of the most fundamental and critical problems in computer vision and image processing. In this paper, we carry out a comprehensive review on image feature information (IFI) extraction techniques for interest point detection. To systematically introduce how the existing interest point detection methods extract IFI from an input image, we propose a taxonomy of the IFI extraction techniques for interest point detection. According to this taxonomy, we discuss different types of IFI extraction techniques for interest point detection. Furthermore, we identify the main unresolved issues related to the existing IFI extraction techniques for interest point detection and any interest point detection methods that have not been discussed before. The existing popular datasets and evaluation standards are provided and the performances for eighteen state-of-the-art approaches are evaluated and discussed. Moreover, future research directions on IFI extraction techniques for interest point detection are elaborated

Wavelet and Multiscale Methods

Various scientific models demand finer and finer resolutions of relevant features. Paradoxically, increasing computational power serves to even heighten this demand. Namely, the wealth of available data itself becomes a major obstruction. Extracting essential information from complex structures and developing rigorous models to quantify the quality of information leads to tasks that are not tractable by standard numerical techniques. The last decade has seen the emergence of several new computational methodologies to address this situation. Their common features are the nonlinearity of the solution methods as well as the ability of separating solution characteristics living on different length scales. Perhaps the most prominent examples lie in multigrid methods and adaptive grid solvers for partial differential equations. These have substantially advanced the frontiers of computability for certain problem classes in numerical analysis. Other highly visible examples are: regression techniques in nonparametric statistical estimation, the design of universal estimators in the context of mathematical learning theory and machine learning; the investigation of greedy algorithms in complexity theory, compression techniques and encoding in signal and image processing; the solution of global operator equations through the compression of fully populated matrices arising from boundary integral equations with the aid of multipole expansions and hierarchical matrices; attacking problems in high spatial dimensions by sparse grid or hyperbolic wavelet concepts. This workshop proposed to deepen the understanding of the underlying mathematical concepts that drive this new evolution of computation and to promote the exchange of ideas emerging in various disciplines

Cyclist Detection, Tracking, and Trajectory Analysis in Urban Traffic Video Data

The major objective of this thesis work is examining computer vision and machine learning detection methods, tracking algorithms and trajectory analysis for cyclists in traffic video data and developing an efficient system for cyclist counting. Due to the growing number of cyclist accidents on urban roads, methods for collecting information on cyclists are of significant importance to the Department of Transportation. The collected information provides insights into solving critical problems related to transportation planning, implementing safety countermeasures, and managing traffic flow efficiently. Intelligent Transportation System (ITS) employs automated tools to collect traffic information from traffic video data. In comparison to other road users, such as cars and pedestrians, the automated cyclist data collection is relatively a new research area. In this work, a vision-based method for gathering cyclist count data at intersections and road segments is developed. First, we develop methodology for an efficient detection and tracking of cyclists. The combination of classification features along with motion based properties are evaluated to detect cyclists in the test video data. A Convolutional Neural Network (CNN) based detector called You Only Look Once (YOLO) is implemented to increase the detection accuracy. In the next step, the detection results are fed into a tracker which is implemented based on the Kernelized Correlation Filters (KCF) which in cooperation with the bipartite graph matching algorithm allows to track multiple cyclists, concurrently. Then, a trajectory rebuilding method and a trajectory comparison model are applied to refine the accuracy of tracking and counting. The trajectory comparison is performed based on semantic similarity approach. The proposed counting method is the first cyclist counting method that has the ability to count cyclists under different movement patterns. The trajectory data obtained can be further utilized for cyclist behavioral modeling and safety analysis

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Radon transforms: Unitarization, Inversion and Wavefront sets

The first contribution of this thesis is a new approach based on the theory of group representations in order to solve in a general an unified way the unitarization and inversion problems for generalized Radon transform associated to dual pairs (G/K,G/H) of homogeneous spaces of a locally compact group G, where K and H are closed subgroups of G. Precisely, under some technical assumptions, if the quasi-regular representations of G acting on L^2(G/K) and L^2(G/H) are irreducible, then the Radon transform, up to a composition with a suitable pseudo-differential operator, can be extended to a unitary operator intertwining the two representations. If, in addition, the representations are square integrable, an inversion formula for the Radon transform based on the voice transform associated to these representations is given. Several examples are discussed. The second purpose of the thesis is to investigate the connection between the shearlet transform and the wavelet transform, which has to be found in the Radon transform in affine coordinates. This link yields a formula for the shearlet transform that involves only integral transforms applied to the affine Radon transform of the signal, thereby opening new perspectives both for finding a new algorithm to compute the shearlet transform of a signal and for the inversion of the Radon transform. Furthermore, we study the role of the Radon transform in microlocal analysis, especially in the resolution of the wavefront set in shearlet analysis. We propose a new approach based on the wavelet transform and on the Radon transform which clarifies how the ability of the shearlet transform to characterize the wavefront set of signals follows directly by the combination of the microlocal properties inhereted by the one-dimensional wavelet transform with a sensitivity for directions inhereted by the Radon transform. Finally, the last chapter of the thesis is devoted to the extension of the shearlet transform to distributions. Our main results are continuity theorems for the shearlet transform and its transpose, called the shearlet synthesis operator, on various test function spaces. Then, we use these continuity results to develop a distributional framework for the shearlet transform via a duality approach. This work arises from the lack in the theory of a complete distributional framework for the shearlet transform and from the link between the shearlet transform with the Radon and the wavelet transforms, whose distribution theory is a deeply investigated and well known subject in applied mathematics

Subdivision schemes for curve design and image analysis

Subdivision schemes are able to produce functions, which are smooth up to pixel accuracy, in a few steps through an iterative process. They take as input a coarse control polygon and iteratively generate new points using some algebraic or geometric rules. Therefore, they are a powerful tool for creating and displaying functions, in particular in computer graphics, computer-aided design, and signal analysis. A lot of research on univariate subdivision schemes is concerned with the convergence and the smoothness of the limit curve, especially for schemes where the new points are a linear combination of points from the previous iteration. Much less is known for non-linear schemes: in many cases there are only ad hoc proofs or numerical evidence about the regularity of these schemes. For schemes that use a geometric construction, it could be interesting to study the continuity of geometric entities. Dyn and Hormann propose sufficient conditions such that the subdivision process converges and the limit curve is tangent continuous. These conditions can be satisfied by any interpolatory scheme and they depend only on edge lengths and angles. The goal of my work is to generalize these conditions and to find a sufficient constraint, which guarantees that a generic interpolatory subdivision scheme gives limit curves with continuous curvature. To require the continuity of the curvature it seems natural to come up with a condition that depends on the difference of curvatures of neighbouring circles. The proof of the proposed condition is not completed, but we give a numerical evidence of it. A key feature of subdivision schemes is that they can be used in different fields of approximation theory. Due to their well-known relation with multiresolution analysis they can be exploited also in image analysis. In fact, subdivision schemes allow for an efficient computation of the wavelet transform using the filterbank. One current issue in signal processing is the analysis of anisotropic signals. Shearlet transforms allow to do it using the concept of multiple subdivision schemes. One drawback, however, is the big number of filters needed for analysing the signal given. The number of filters is related to the determinant of the expanding matrix considered. Therefore, a part of my work is devoted to find expanding matrices that give a smaller number of filters compared to the shearlet case. We present a family of anisotropic matrices for any dimension d with smaller determinant than shearlets. At the same time, these matrices allow for the definition of a valid directional transform and associated multiple subdivision schemes

Image Analysis via Applied Harmonic Analysis : Perceptual Image Quality Assessment, Visual Servoing, and Feature Detection

Certain systems of analyzing functions developed in the field of applied harmonic analysis are specifically designed to yield efficient representations of structures which are characteristic of common classes of two-dimensional signals, like images. In particular, functions in these systems are typically sensitive to features that define the geometry of a signal, like edges and curves in the case of images. These properties make them ideal candidates for a wide variety of tasks in image processing and image analysis. This thesis discusses three recently developed approaches to utilizing systems of wavelets, shearlets, and alpha-molecules in specific image analysis tasks. First, a perceptual image similarity measure is introduced that is solely based on the coefficients obtained from six discrete Haar wavelet filters but yields state of the art correlations with human opinion scores on large benchmark databases. The second application concerns visual servoing, which is a technique for controlling the motion of a robot by using feedback from a visual sensor. In particular, it will be investigated how the coefficients yielded by discrete wavelet and shearlet transforms can be used as the visual features that control the motion of a robot with six degrees of freedom. Finally, a novel framework for the detection and characterization of features such as edges, ridges, and blobs in two-dimensional images is presented and evaluated in extensive numerical experiments. Here, versatile and robust feature detectors are obtained by exploiting the special symmetry properties of directionally sensitive analyzing functions in systems created within the recently introduced alpha-molecule framework