Holomorphic filters for object detection

Abstract: It is well known that linear filters are not powerful enough for many low-level image processing tasks. But it is also very difficult to design robust non-linear filters that respond exclusively to features of interest and that are at the same time equivariant with respect to translation and rotation. This paper proposes a new class of rotation-equivariant non-linear filters that is based on the principle of group integration. These filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of the intermediate results. Our experiments show that the proposed filter detects pollen porates with only half as many errors than alternative approaches, when high localization accuracy is required.