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

2. 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

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

4. 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.

5. 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

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

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

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