Unified approach to exact geometric computation over integer points

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We focused on 2D rotations on grid points computed by using only integers. We investigated rotation angles with any of which a given digital image is rotated to the same digital image. We then proposed a method for obtaining the upper and lower bounds of such angles from a given Euclidean angle and from a pair of digital images. Furthermore, we extended this method so that it can deal with 3D rotations. Namely, we studied the intersection between the 3D half-grid and the rotation plane and proposed 3D hinge angles. Then, we developed a method to sort all 3D hinge angles with integer computations alone. This investigation is extended to rigid transformations. In addition, we addressed the problem of fitting a discrete line or polynomial curve to given integer points in the presence of outliers. We then proposed a method that effectively achieves a locally optimal solution by using a local search