Recursive Implementation of Anisotropic Filtering Zeyun Yu Department of Computer Science University of Texas at Austin

Isotropic Filtering Recursive Implementation of the Gaussian Filter [Young et al, 1995] Forward: Backward: n n-1 n-2 n-3 n+2 n+1 n+3

Anisotropic Filtering: Goal The goal: one-dimensional example Input Isotropic What we want ! Smooth noise but preserving sharp edges !

Anisotropic Filtering: Method Local maximum, minimum and average Local maximum Local minimum Local average Making decision: If (in >= lcavg) out = lcmax; If (in < lcavg) out = lcmin; where in = input signal; out = output signal. lcmax, lcmin and lcavg are computed local maximum, minimum and average, respectively.

Anisotropic Filtering: Method (contd.) Extension to higher dimension Perform the above method on each dimension Row first Then column Note: It turns out that the order of row and column makes little difference on results

Results top-left: original image top-right: isotropic filtering bottom-left: proposed method bottom-right: Perona method

Results (contd.) left: original image middle: isotropic filtering Right-top: proposed method Right-bottom: Perona method

Time Analysis Horizontal: size of images (each dimension); Vertical: time in seconds