Abstract: The property of smoothing while preserving edges makes the bilateral filter a very popular image processing tool. However, its non-linear nature results in a computationally costly operation. Various works propose fast approximations to the bilateral filter. However, the majority does not generalize to vector input as is the case with color images. We propose a fast approximation to the bilateral filter for color images. The filter is based on two ideas. First, the number of colors, which occur in a single natural image, is limited. We exploit this color sparseness to rewrite the initial non-linear bilateral filter as a number of linear filter operations. Second, we impose a statistical prior to the image values that are locally present within the filter window. We show that this statistical prior leads to a closed-form solution of the bilateral filter. Finally, we combine both ideas into a single fast and accurate bilateral filter for color images. Experimental results show that our bilateral filter based on the local prior yields an extremely fast bilateral filter approximation, but with limited accuracy, which has potential application in real-time video filtering. Our bilateral filter, which combines color sparseness and local statistics, yields a fast and accurate bilateral filter approximation and obtains the state-of-the-art results.

Abstract: Motion perception is an amazing innate ability of the creatures on the planet. This adroitness entails a functional advantage that enables species to compete better in the wild. The motion perception ability is usually employed at different levels, allowing from the simplest interaction with the ’physis’ up to the most transcendental survival tasks. Among the five classical perception system , vision is the most widely used in the motion perception field. Millions years of evolution have led to a highly specialized visual system in humans, which is characterized by a tremendous accuracy as well as an extraordinary robustness. Although humans and an immense diversity of species can distinguish moving object with a seeming simplicity, it has proven to be a difficult and non trivial problem from a computational perspective. In the field of Computer Vision, the detection of moving objects is a challenging and fundamental research area. This can be referred to as the ’origin’ of vast and numerous vision-based research sub-areas. Nevertheless, from the bottom to the top of this hierarchical analysis, the foundations still relies on when and where motion has occurred in an image. Pixels corresponding to moving objects in image sequences can be identified by measuring changes in their values. However, a pixel’s value (representing a combination of color and brightness) could also vary due to other factors such as: variation in scene illumination, camera noise and nonlinear sensor responses among others. The challenge lies in detecting if the changes in pixels’ value are caused by a genuine object movement or not. An additional challenging aspect in motion detection is represented by moving cast shadows. The paradox arises because a moving object and its cast shadow share similar motion patterns. However, a moving cast shadow is not a moving object. In fact, a shadow represents a photometric illumination effect caused by the relative position of the object with respect to the light sources. Shadow detection methods are mainly divided in two domains depending on the application field. One normally consists of static images where shadows are casted by static objects, whereas the second one is referred to image sequences where shadows are casted by moving objects. For the first case, shadows can provide additional geometric and semantic cues about shape and position of its casting object as well as the localization of the light source. Although the previous information can be extracted from static images as well as video sequences, the main focus in the second area is usually change detection, scene matching or surveillance. In this context, a shadow can severely affect with the analysis and interpretation of the scene. The work done in the thesis is focused on the second case, thus it addresses the problem of detection and removal of moving cast shadows in video sequences in order to enhance the detection of moving object.