A Method For 2D Image Deformation Based On Geometric Shape

Image deformation, which is widely used in areas such as image edition, animation, filmdom, enriching graphical user interfaces and so on, is a transformation of geometric shape that occurs in an image itself or between two different images. Along with the development of computer technology, it seems possible to deform images by computer, thus, welcoming the age of research work on methods for image deformation. Nowadays, the technology of image deformation has grown to be one of the most important parts in computer graphics.These years, 2D image deformations have been a hot topic and great achievements have been made at present. It can mainly be divided into several aspects, for example, Free-Form Deformations, skeleton-based techniques, physically-based simulations and point-based algorithms as well. Among them, the point-based deformation technique has the advantage of simply operating and running effectively, therefore, it becomes the major class for the research of 2D image deformation. In this paper, we still focus on the point-based deformation but propose a novel method for 2D image deformations based on geodesic distance within a polygon. Here is how the new algorithm works: firstly, computing the geodesic distance between every pixel in the image to be deformed and every control point; secondly, considering the geodesic distance as the weight by which one control point affects one pixel; thirdly, getting the new position for each pixel by applying the moving least squares algorithm to it, and finally rendering the deformed image.Since Euclidean distance only reflects the spacial relationship between each pixel and control point, the Affine transformation with Euclidean distance as the weight usually causes undesirable deformation in local area nearby control points. Instead, geodesic distance in this paper takes the geometric shape of an image into account, showing the positional relationship of each pixel and control point inside the image. Then, the method presented in this paper can effectively avoid the error deformation mentioned above.After testing a large number of images, we come to a conclusion that our method is not only intuitive and more natural but also able to locally deform and modify an image.