Pyramid Image and Resize Based on Spline Model

P. Prystavka, O. Cholyshkina
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引用次数: 2

Abstract

: 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.
基于样条模型的金字塔图像和大小调整
本文的基础是将图像模型形式化为b样条的线性组合,这接近于插值。作者平均给出了其相应的显式方面和低频滤波和缩放算子。本文演示了获得缩放到任意(不一定是整数)次数的数字图像的可能性,并提供了相应的算法。文中给出了指示样条模型的逼近质量估计的实例。此外,本文还给出了引入该模型作为众所周知的基于二维高斯函数的图像模型的替代方法的理由。我们注意到,随着阶数的增加,b样条曲线与高斯曲线的差异很小,而且它们的计算更简单,使得样条曲线模型具有研究和应用的吸引力。将众所周知的形式化方法应用于基于高斯函数的数字图像金字塔的构建,作者建议将其扩展到样条模型的情况。图像金字塔的使用取决于在数字图像中寻找特殊点的任务,以便确定不同数字照片中同一物体的图像之间的明确对应关系。本文给出了构造金字塔的基于2-6阶b样条的线性算子,并举例说明了它们的用法。基于光栅与可变系数掩模的卷积,本文论证了获得缩放到任意(不一定是整数)次数的数字图像的可能性,并提供了相应的算法。最后给出了基于该算法的图像大小调整的实例。作者相信,在未来的论文中进行的研究将允许数字图像获得更多计算简单的算法来确定特殊点及其检测器。论文结果:1;在二维多项式样条的基础上,在平均接近插值的2 - 6阶b样条的基础上,形式化了一个DI的模型。2. 给出了基于样条模型的低频DI滤波卷积算子。3.提供了用于构建图像金字塔的缩放算子,以便进一步搜索特殊点。4. 提出了一种基于连续样条近似将DI缩放到任意整数次的算法。5. 基于样条模型的数字图像缩放算法允许您在任意(不一定是整数)次数更改图像的大小,不同之处在于它提供了高缩放精度,并且由于样条模型的高近似属性和平滑性而没有伪影;与基于二维高斯函数的模型相比,该缩放算法以最少的简单数学运算实现了最优的计算方案,从而使数字图像处理具有较高的计算速度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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