In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

Several important pattern recognition applications are based on feature extraction and vector clustering. Directional patterns may be represented by rotation-variant directional vectors, formed from M features uniformly extracted in M directions. It is often required that pattern recognition algorithms are invariant under pattern rotation or, equivalently, invariant under circular shifts of suc...

Non-local means is a recently proposed denoising technique that better preserves image structures than other methods. However, the computational cost of non-local means is prohibitive, especially for large 3D images. Modifications have previously been proposed to reduce the cost, which result in image artefacts. This paper proposes a compact rotation invariant descriptor. Testing demonstrates i...