Towards High Quality Gradient Estimation on Regular Lattices Our work is titled “Towards High Quality Gradient Estimation On Regular Lattices” And the authors are myself Zahid Hossain, Usman Raza Alim and Dr. Torsten Moller Zahid Hossain, Usman Raza Alim and Dr. Torsten Möller

Our Contributions Problem: Derivative Estimation Taylor Series Small Support Problem: Derivative Estimation Very accurate Taylor Series Framework Orthogonal Projection Framework “Derivative Estimation” is a fundamental problem in visualization. First derivative, or the gradient, is used for shading surfaces while other higher derivatives are used for measuring quantities like curvatures and so forth. Not only we have to estimate these derivatives but also estimate them for arbitrary lattices and dimensions. But how good are our derivative estimators ? We address this problem and we developed two separate frameworks. The first one is “Taylor Series Framework” where filters have small support with reasonable rendering quality. This method is good for on-the-fly computations. And the second one is “Orthogonal Projection Framework,” based on ideas from approximation theory, which yields very accurate results but requires pre-processing as the filter support is much larger. We then extended both the frameworks for all regular lattices in arbitrary dimensions and for accuracy requirements. Extended to all regular lattices in Rn: CC, BCC … CC BCC

Comparison: In BCC Grid High Res. Here we compare our methods with Karp dataset in BCC Grid. We zoom into the gill region of the fish. The image on the top-right is rendered using very high resolution dataset to give an intuition of how things should look like. The image below is using a low resolution dataset. This one is shaded with gradients estimated using the existing method, simple 2nd order central differencing. This one is shaded using our new Taylor series framework And the last one uses our new Orthogonal Projection framework which improves image quality quite dramatically! For more details we invite you to visit our poster, Thank you. Low Res. Our Method: Orthogonal Projection Framework Existing Method: 2nd-CD Our Method: Taylor Series Framework