Abstract: A scattered spherical harmonic (SH) approximation method is proposed for pre-computation of SH coefficients at sampling vertices of an object to be rendered. The approach sparsely populates the object with a plurality of SH sampling vertices and uses the least squares approximation to calculate the SH coefficients at any (other) arbitrary point of the object by extrapolating from the computed SH coefficients at the SH sampling vertices.

Abstract: Systems and methods image zooming with intensity preservation is disclosed. In one aspect, embodiments of the present disclosure include a method, which may be implemented on a system, of minimizing energy levels over a set of high-resolution image pixels of a high-resolution image via total variational filtering to obtain the high-resolution image from at least a portion of a low-resolution image; the low-resolution image having a first energy level, the high resolution image having a second energy level, and the first energy level to be substantially similar in value as the second energy level. One embodiment can include, determining a pixel value of a particular high-resolution image pixel based on the pixel values of a plurality of pixels of the at least a portion of the low-resolution image and the pixel values of the high-resolution image pixels not including the particular high-resolution image pixel.

Abstract: Systems and methods image zooming with intensity preservation is disclosed. In one aspect, embodiments of the present disclosure include a method, which may be implemented on a system, of minimizing energy levels over a set of high-resolution image pixels of a high-resolution image via total variational filtering to obtain the high-resolution image from at least a portion of a low-resolution image; the low-resolution image having a first energy level, the high resolution image having a second energy level, and the first energy level to be substantially similar in value as the second energy level. One embodiment can include, determining a pixel value of a particular high-resolution image pixel based on the pixel values of a plurality of pixels of the at least a portion of the low-resolution image and the pixel values of the high-resolution image pixels not including the particular high-resolution image pixel.

Abstract: A method and system for variational and iterative fitting of complex curves (such as Super Helix curves) to arbitrary regular parametric curves is described, called a curve fitting system. The curve fitting system uses data reduction and error-analysis often found in mesh decimation schemes as well as non-linear minimization. The curve fitting system takes full advantage of the large body of existing work on parametric curve modeling, while utilizing new and beneficial curve models for simulation.

Abstract: A scattered spherical harmonic (SH) approximation method is proposed for pre-computation of SH coefficients at sampling vertices of an object to be rendered. The approach sparsely populates the object with a plurality of SH sampling vertices and uses the least squares approximation to calculate the SH coefficients at any (other) arbitrary point of the object by extrapolating from the computed SH coefficients at the SH sampling vertices.