Triangle meshes can provide an effective geometric representation of images. Although many mesh generation methods have been proposed to date, many of them do not explicitly take image discontinuities into consideration. In this thesis, a new mesh model for images, which explicitly represents discontinuities (i.e., image edges), is proposed along with two corresponding mesh-generation methods that determine the mesh-model parameters for a given input image. The mesh model is based on constrained Delaunay triangulations (DTs), where the constrained edges correspond to image edges. One of the proposed methods is named explicitly-represented discontinuities-with error diffusion (ERDED), and is fast and easy to implement. In the ERDED method, the error diffusion (ED) scheme is employed to select a subset of sample points that are not on the constrained edges. The other proposed method is called ERDGPI. In the ERDGPI method, a constrained DT is first constructed with a set of prespecified constrained edges. Then, the greedy point insertion (GPI) scheme is employed to insert one point into the constrained DT in each iteration until a certain number of points is reached. The ERDED and ERDGPI methods involve several parameters which must be provided as input. These parameters can affect the quality of the resulting image approximations, and are discussed in detail. We also evaluate the performance of our proposed ERDED and ERDGPI methods by comparing them with the highly effective ED and GPI schemes. Our proposed methods are demonstrated to be capable of producing image approximations of higher quality both in terms of PSNR and subjective quality than those generated by other schemes. For example, the reconstructed images produced by the proposed ERDED method are often about 3.77 dB higher in PSNR than those produced by the ED scheme, and our proposed ERDGPI scheme produces image approximations of about 1.08 dB higher PSNR than those generated by the GPI approach. / Graduate

Mobile robotics has been very discussed and wide spread topic recently.   This due to the development in the computer technology that allows us to create   better and more sophisticated robots. The goal of this effort is to create robots   that will be able to autonomously move in the chosen environment. To achieve this goal,   it is necessary for the robot to create the map of its environment, where   the motion planning will occur. Nowadays, the probabilistic algorithms based   on the SLAM algorithm are considered standard in the mapping in these times.   This Phd. thesis deals with the proposal of the motion planning of the robot with   stereocamera placed on the pan-and-tilt unit. The motion planning is designed with   regard to the use of algorithms, which will look for the significant features   in the pair of the images. With the use of the triangulation the map, or a model will be created.     The benefits of this work can be divided into three parts. In the first one the way   of marking the free area, where the robot will plan its motion, is described. The second part   describes the motion planning of the robot in this free area. It takes into account   the properties of the SLAM algorithm and it tries to plan the exploration in order to create   the most precise map. The motion of the pan-and-tilt unit is described in the third part.   It takes advantage of the fact that the robot can observe places that are in the different   directions than the robot moves. This allows us to observe much bigger space without   losing the information about the precision of the movements.