ÐDetermining the rigid transformation relating 2D images to known 3D geometry is a classical problem in photogrammetry and computer vision. Heretofore, the best methods for solving the problem have relied on iterative optimization methods which cannot be proven to converge and/or which do not effectively account for the orthonormal structure of rotation matrices. We show that the pose estimation problem can be formulated as that of minimizing an error metric based on collinearity in object (as opposed to image) space. Using object space collinearity error, we derive an iterative algorithm which directly computes orthogonal rotation matrices and which is globally convergent. Experimentally, we show that the method is computationally efficient, that it is no less accurate than the best currently employed optimization methods, and that it outperforms all tested methods in robustness to outliers.
We study the relation of neural development, organization, and activity to behavior. We provide a model of the locomotive oscillator, a neural system supplying alternating stimulation to extensor and flexor muscles creating an oscillatory motion. We propose a protocol by which this neural system starting from unstructured, unconnected neural populations develops structure and function. The protocol is studied by both computer simulation and mathematical analysis. Our main results are 1. The locomotive oscillator self-organizes and maintains its organization, assuming certain properties of the neural populations. 2. Imperfections disturbing the functional adequacy of the neural populations may lead to the deterioration and disappearance of the oscillatory behavior. 3. The locomotive oscillator may fail to organize if the development is not staged in time.
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