Image Segmentation with Eigenfunctions of an Anisotropic Diffusion Operator

We propose the eigenvalue problem of an anisotropic diffusion operator for image segmentation. The diffusion matrix is defined based on the input image. The eigenfunctions and the projection of the input image in some eigenspace capture key features of the input image. An important property of the model is that for many input images, the first few eigenfunctions are close to being piecewise constant, which makes them useful as the basis for a variety of applications such as image segmentation and edge detection. The eigenvalue problem is shown to be related to the algebraic eigenvalue problems resulting from several commonly used discrete spectral clustering models. The relation provides a better understanding and helps developing more efficient numerical implementation and rigorous numerical analysis for discrete spectral segmentation methods. The new continuous model is also different from energy-minimization methods such as geodesic active contour in that no initial guess is required for in the current model. The multi-scale feature is a natural consequence of the anisotropic diffusion operator so there is no need to solve the eigenvalue problem at multiple levels. A numerical implementation based on a finite element method with an anisotropic mesh adaptation strategy is presented. It is shown that the numerical scheme gives much more accurate results on eigenfunctions than uniform meshes. Several interesting features of the model are examined in numerical examples and possible applications are discussed

Model-Based Edge Detector for Spectral Imagery Using Sparse Spatiospectral Masks

Two model-based algorithms for edge detection in spectral imagery are developed that specifically target capturing intrinsic features such as isoluminant edges that are characterized by a jump in color but not in intensity. Given prior knowledge of the classes of reflectance or emittance spectra associated with candidate objects in a scene, a small set of spectral-band ratios, which most profoundly identify the edge between each pair of materials, are selected to define a edge signature. The bands that form the edge signature are fed into a spatial mask, producing a sparse joint spatiospectral nonlinear operator. The first algorithm achieves edge detection for every material pair by matching the response of the operator at every pixel with the edge signature for the pair of materials. The second algorithm is a classifier-enhanced extension of the first algorithm that adaptively accentuates distinctive features before applying the spatiospectral operator. Both algorithms are extensively verified using spectral imagery from the airborne hyperspectral imager and from a dots-in-a-well midinfrared imager. In both cases, the multicolor gradient (MCG) and the hyperspectral/spatial detection of edges (HySPADE) edge detectors are used as a benchmark for comparison. The results demonstrate that the proposed algorithms outperform the MCG and HySPADE edge detectors in accuracy, especially when isoluminant edges are present. By requiring only a few bands as input to the spatiospectral operator, the algorithms enable significant levels of data compression in band selection. In the presented examples, the required operations per pixel are reduced by a factor of 71 with respect to those required by the MCG edge detector

Moving-edge detection via heat flow analogy

In this paper, a new and automatic moving-edge detection algorithm is proposed, based on using the heat flow analogy. This algorithm starts with anisotropic heat diffusion in the spatial domain, to remove noise and sharpen region boundaries for the purpose of obtaining high quality edge data. Then, isotropic and linear heat diffusion is applied in the temporal domain to calculate the total amount of heat flow. The moving-edges are represented as the total amount of heat flow out from the reference frame. The overall process is completed by non-maxima suppression and hysteresis thresholding to obtain binary moving edges. Evaluation, on a variety of data, indicates that this approach can handle noise in the temporal domain because of the averaging inherent of isotropic heat flow. Results also show that this technique can detect moving-edges in image sequences, without background image subtraction