2D Image data approximation using Savitzky Golay filter — Smoothing and differencing

Smoothing and differencing is one of the major important and necessary step in the field of signal processing, image processing and also in the field on analytical chemistry. The search for an efficient image smoothing and edge detection method is a challenging task in image processing sector. Savitzky Golay Filters are one among the widely used filters for analytical chemistry. Even though they have exceptional features, they are rarely used in the field of image processing. The designed filter is applied for image smoothing and a mathematical model based on partial derivatives is proposed to extract the edges in images. The smoothing technique of SG filter offers an extremely simple aid in extracting the edge information. An approach using SG filter which can be applied in preserving edge information is one of the major tasks involved in the classification process in the domain of Optical Character Recognition. The paper is focused on designing the Savitzky Golay filter by using the concepts of linear algebra. The main objective of the paper is to portray a clear cut idea about Savitzky Golay filter and to study the design of Savitsky Golay filters based on the concepts of Linear Algebra.