In this paper, we present an edge detection method based on the thin-plate s pline with tension. Under regularization theory, the image is represented in a convolution from between the original image data and a two-dimensional kernel. TShis convolution kernel is deviced from a PDE, which is related to a second order (thin-plate or bending) term and a first order (membrance or tension) term. TRhis image representation involves two parameters: a smoothing parameter (or scale parameter) and a weighted smoothness parameter (which controls the degrees of the continuity of the reconstruction by placing a different weighting on the thin-plate and tension terms). By tuning these parameters, the image can be represented at different scales and with different smoothness requirements. Based on this convolution representation, the edges can be detected by differentiating the image to look for the zero-corossings of the Laplacian. By tuning the values of these two parameters, the edges at the different scales will be extracted.
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