Pyramid Image and Resize Based on Spline Model

The paper is based around the formalization of the image model as a linear combination of B-splines, which is close to interpolation. The authors present, on average, its corresponding explicit aspects and low-frequency filtering and scaling operators. The possibility to obtain digital images scaled to an arbitrary, not necessarily integer, number of times is demonstrated in the article and the corresponding algorithm is provided. The article provides with the examples on estimation of the quality of approximation of the indicated spline model. Also there are given grounds for its introduction as an alternative to the well-known image model based on the two-dimensional Gaussian function. It is noted that with the increasing order, B-splines differ little from Gaussian, and their simpler calculation makes the spline model attractive for research and use. Applying the well-known formalization of the approach to the construction of a pyramid of digital images based on Gaussian functions, the authors suggest its extension onto the case of a spline model. The use of image pyramids is conditioned by the task of finding special points in a digital image in order to determine the unambiguous correspondence between the images of the same object in different digital photographs. The paper presents linear operators based on B-splines of 2-6 orders aimed at the construction of a pyramid, it also demonstrates an example of their usage. Based on the convolution of the raster with a mask with variable coefficients the possibility to obtain digital images scaled to an arbitrary, not necessarily integer, number of times is demonstrated in the article and the corresponding algorithm is provided. Image resizing based on the suggested algorithm is also demonstrated by examples. The authors believe that the research conducted in the paper in the future will allow for digital images to obtain more computationally simple algorithms for determining special points and their detectors. Results of paper: 1. The model of a DI has been formalized on the basis of two-dimensional polynomial splines, on the basis of B-splines of the second-sixth orders which are close to interpolation on the average. 2. The convolution operators of low-frequency DI filtering based on the spline model are presented. 3. Provided are the scaling operators used to build image pyramids, in order to further search for special points. 4. An algorithm for scaling the DI to an arbitrary, not necessarily an integer number of times based on a continuous spline approximation has been suggested. 5. Algorithm for scaling a digital image based on a spline model allows you to change the size of the image in any (not necessarily an integer) number of times, differs in that it provides high scaling accuracy and no artifacts due to high approximate properties and smoothness of the spline model;6. The scaling algorithm allows digital image processing at high computational speed due to the optimal computational scheme with a minimum of simpler mathematical operations, compared with models based on the two-dimensional Gaussian function.