Rotations in the discrete plane are important for many applications such as image matching or construction of mosaic images. We suppose that a digital image A is transformed to another digital image B by a rotation. In the discrete plane, there are many angles giving the rotation from A to B, which we called admissible rotation angles from A to B. For such a set of admissible rotation angles, there exist two angles that achieve the lower and the upper bounds. To find those lower and upper bounds, we use hinge angles as used in [7]. A sequence of hinge angles is a set of particular angles determined by a digital image in the sense that any angle between two consecutive hinge angles gives the identical rotation of the digital image. We propose a method for obtaining the lower and the upper bounds of admissible rotation angles using hinge angles from a given Euclidean angle or from a pair of corresponding digital images.

International audienceIn this paper, we study 3D rotations on grid points computed by using only integers. For that purpose, we investigate the intersection between the 3D half-grid and the rotation plane. From this intersection, we define 3D hinge angles which determine a transit of a grid point from a voxel to its adjacent voxel during the rotation. Then, we give a method to sort all 3D hinge angles with integer computations. The study of 3D hinge angles allows us to design a 3D discrete rotation and to estimate the rotation between a pair of digital images in correspondence

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This paper proposes a method of retrieving texture from images containing pattern used for one shot 3D scanning system based on a grid pattern. Range scanners using projector-camera systems can be used for real-time 3D scanning with accurate results and at a low cost. However, these techniques cannot retrieve color information from the captured object since to obtain the best results, they require dark environments and the projection on the object to reconstruct dense and bright lines pattern masks most of the object textures. Therefore, we propose a technique of slightly modifying the input of a given 3D scanning system in order to have bright images with texture information and then retrieve the textures of the object using an inpainting method. The presented method adapts simple algorithms such as Canny filter and patches based inpainting in order to obtain a fully automatic method that does not require any user intervention.