This paper describes two methods for constructing a depth map from images. Each method has two stages. First, one or more needle maps are determined using a pair of images. This process employs either the Marr-Poggio-Grimson stereo and shape-from-shading, or, instead, photometric stereo. Secondly, a depth map is constructed from the needle map or needle maps computed by the first stage. Both methods make use of an iterative relaxation method to obtain the final depth map.

This dissertation investigates optimization approaches applied to radiation therapy in cancer treatment. Since cancerous cells are surrounded by critical organs and normal tissues, there is conflicting objectives in the treatment design of providing sufficient radiation dose to tumor region, while avoiding normal healthy cells. In general, the goal of radiation therapy is to conform the spatial distribution of the prescribed dose to the tumor volume while minimizing the dose to the surrounding normal structures. A recent advanced technology, using multi-leaf collimator integrated into linear accelerator, provides much better opportunities to achieve this goal: the radiotherapy based on non-uniform radiation beams intensities is called Intensity-Modulated Radiation Therapy. My dissertation research offers a quadratic mixed integer programming approach to determine optimal beam orientations and beamlets intensity simultaneously. The problems generated from real patient cases are large-scale dense instances due to the physics of dose contributions from beamlets to volume elements. The research highlights computational techniques to improve solution times for these intractable instances. Furthermore, results from this research will provide plans that are clinically acceptable and superior in plan quality, thus directly improve the curity rate and lower the normal tissue complication for cancer patients.