For accurate prediction of normal tissue tolerance, it is important that the volumetric information of dose distribution be considered. However, in dosimetric optimization of intensity modulated beams, the dose-volume factor is usually neglected. In this paper we describe two methods of volume-dependent optimization for intensity modulated beams such as those generated by computer-controlled multileaf collimators. The first method uses a volume sensitive penalty function in which fast simulated annealing is used for cost function minimization (CFM). The second technique is based on the theory of projections onto convex sets (POCS) in which the dose-volume constraint is replaced by a limit on integral dose. The ability of the methods to respect the dose-volume relationship was demonstrated by using a prostate example involving partial volume constraints to the bladder and the rectum. The volume sensitive penalty function used in the CFM method can be easily adopted by existing optimization programs. The convex projection method can find solutions in much shorter time with minimal user interaction.

The primary goal in motion vision is to extract information about the motion and shape of an object in a scene that is encoded in the optic flow. While many solutions to this problem, both iterative and in closed form, have been proposed, practitioners still view the problem as unsolved, since these methods, for the most part, cannot deal with some important aspects of realistic scenes. Among these are comlex unsegmented scenes, nonsmooth objects, and general motion of the camera. In addition, the performance of many methods degrades ungracefully as the quality of the data deteriorates.Here, we will derive a closed-form solution for motion estimation based on the first-order information from two image regions with distinct flow "structures." A unique solution is guaranteed when these corespond to two surface patches with different normal vectors. Given an image sequence, we will show how the image may be segmented into regions with the necessary properties, optical flow is computed for these regions, and motion parameters are calculated. The method can be applied to arbitrary scenes and any camera motion. We will show theoretically why the method is more robust than other proposed techniques that require the knowledge of the full flow or information up to the second-order terms of it. Experimental results are presented to support the theoretical derivations.

Abstract. Synthesis of beam profiles for a given dose prescription is a central problem in radiotherapy. Care must be taken in the beam design to expose the tumour volume at a high level, to avoid significant irradiation of critical organs, and to minimize exposure of all other tissue. Use of the synthesis procedure known as alternating projections onto convex sets (POCS) is shown to be a viable approach to beam design. POCS is a powerful tool for signal and image restoration and synthesis. Convex sets of signals obeying desired constraint sets are first specified. Then, by repeated projections onto these sets, convergence is to a signal obeying all desired constraints if the constraint sets have a finite intersection. In this paper we apply the method of POCS to conformal radiotherapy dose computation. The performance of the method is shown through three representative examples.

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