We explicitly perform some steps of a 3-descent algorithm for the curves $y^2=x^3+a$, $a$ a nonzero integer. In general this will enable us to bound the order of the 3-Selmer group of such curves.
This paper presents a new approach to 3D object recognition by using an Octree model library (OML) I, II and fast search algorithm. The fast search algorithm is used for finding the 4 pairs of feature points to estimate the viewing direction uses on effective two level database. The method is based on matching the object contour to the reference occluded shapes of 49, 118 viewing directions. The initially bestmatched viewing direction is calibrated by searching for the 4 pairs of feature points between the input image and the image projected along the estimated viewing direction. At this point, the input shape is recognized by matching it to the projected shape. The computational complexity of the proposed method is shown to be O(n^2) in the worst case, and that of the simple combinatorial method of O(m^4,n^2), where n and m denote the number of feature points of the 3D model object and the 2D object, respectively.