In many vision problems, rotation-invariant analysis is necessary or preferred. Popular solutions are mainly based on pose normalization or brute-force learning, neglecting the intrinsic properties of rotations. In this paper, we present a rotation invariant detection approach built on the equivariant filter framework, with a new model for learning the filtering behavior. The special properties of the harmonic basis, which is related to the irreducible representation of the rotation group, directly guarantees rotation invariance of the whole approach. The proposed kernel weighted mapping ensures high learning capability while respecting the invariance constraint. We demonstrate its performance on 2D object detection with in-plane rotations, and a 3D application on rotation-invariant landmark detection in microscopic volumetric data.

We propose an algorithm for 3-D multiview deblurring using spatially variant point spread functions (PSFs). The algorithm is applied to multiview reconstruction of volumetric microscopy images. It includes registration and estimation of the PSFs using irregularly placed point markers (beads). We formulate multiview deblurring as an energy minimization problem subject to L1-regularization. Optimization is based on the regularized Lucy-Richardson algorithm, which we extend to deal with our more general model. The model parameters are chosen in a profound way by optimizing them on a realistic training set. We quantitatively and qualitatively compare with existing methods and show that our method provides better signal-to-noise ratio and increases the resolution of the reconstructed images.