Facet models are one of the most fundamental tools in image processing. Minimization of error between the underlying gray level and the observed data from the image forms the basis of facet models. It can be used in a variety of image processing applications, e.g., edge detection, image segmentation, optical flow, etc. However, the computational requirement to support this algorithm is extensive and increases rapidly as the order of the model increases. Our focus has been on faster computation of facet parameters and related factors like local moments. An approach that speeds up the execution time by reducing the redundancies that exist among the kernels is presented. The new algorithm improves the performance by a factor of 7 over direct implementation on a SUN SparcStation 10/41 for estimating six parameters of the quadratic facet model. The performance of this algorithm was also analyzed for the MediaStation 5000, which is a high-performance desktop multimedia system. Optimized implementation on the MediaStation 5000 achieves performance improvement of 38 times over the SUN SparcStation 10/41 implementation.