A Topology Based Denoising Approach for 2D Scalar Fields

A new denoising technique based on the multi-level dissipation element (ML-DE) structure is proposed. A dissipation element (DE) is defined as collection of spatial points whose gradient trajectories share the same pair of extremal points. The entire space can be decomposed into space-filling DEs. From the concept of multi-level extremal points, such a DE structure can be extended to different scale levels. The general idea of image smoothing is realized via smoothing each decomposed DE, remaining the function values at the critical points (maximal, minimal and saddle points) unchanged, from which the key features of the original image can be preserved. The test example of spiky map topology justifies the efficiency and effectiveness of this newly proposed method.