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 [31], the algorithms can be divided into two categories. First, application of hand-crafted image features and of a classifier trained on these features [28, 99, 130]. Second, methods using Convolutional Neural Networks in which features are learned during the training phase [9, 32, 127]. Our aim is to study how both of these types of procedures can be further improved by the incorporation of a framework for image analysis which has a comprehensive theoretical basis. We choose the multi-scale framework of shearlets since it guarantees a unified treatment of the continuum and the digital world [74]. In theory, shearlets provide optimally sparse approximations of certain image models [52, 76] and the ability to characterize edges in images [53, 78]. Moreover, they have been successfully applied practically in several image processing tasks, for example denoising [35, 86] and edge detection [125]. We adapt the shearlet framework according to the requirements of the practical application of a pedestrian detection algorithm. The particular shearlet design consists of two parts. First, the usage of a specific mother shearlet that can precisely locate structures in images. Second, the setup of a shearlet system allowing a uniformly distributed directional analysis and flexible adjustment of the shearlets used per scale. The last point is useful to gain control over the space size of the image features used for pedestrian detection. We show that our shearlet system forms a frame for L2(R2) and provide the conditions required for it. Next, we examine the capability of our shearlet design for edge detection from a theoretical point of view. We show that the designed shearlets can characterize edge points in R2 and their type by the decay rates and the limits of the shearlet transform for decreasing scales. In contrast to the existing literature, we derive decay rates depending on the degree of anisotropy α. For the special case of α = 1/2, we find explicit limits of the shearlet transform which has not been achieved with recently used shearlets. Furthermore, we show that a shearlet mother function with just one vanishing moment is required for our theoretical results. Finally, we illustrate that this requirement is in harmony with the observations made in the practical application of an edge detection algorithm with shearlets. Given our specialized shearlet design, we define meaningful, hand-crafted image features based on the shearlet transform. Meaningful in a sense that the features provide rich information about an object’s structure. The consideration of shearlets has several advantages compared to other image features. At first, they provide a sparse representation of the image, i.e. the result of the shearlet transform only has magnitude with considerably high absolute value at pixels that correspond to edge points. Second, due to the multi-scale framework of shearlets, the structure of objects can directly be investigated at different scales. We show that our shearlet features provide the best results of hand-crafted image features in the Caltech benchmark.