A nonlinear elasticity model for comparing images is formulated and analyzed, in which optimal transformations between images are sought as minimizers of an integral functional. The existence of minimizers in a suitable class of homeomorphisms between image domains is established under natural hypotheses. We investigate whether for linearly related images the minimization algorithm delivers the linear transformation as the unique minimizer.

翻译：建立并分析了一种用于图像比较的非线性弹性模型，其中图像间的最优变换被定义为某一积分泛函的极小值。在自然假设条件下，证明了图像域之间同胚映射的适定类中存在极小值。本文探讨了在线性相关图像的情况下，该极小化算法是否将线性变换作为唯一极小值输出。