This research addresses the design of intensity-curvature functional (ICF) based digital high pass filter (HPF). ICF is calculated from bivariate cubic B-spline model polynomial function and is called ICF-based HPF. In order to calculate ICF, the model function needs to be second order differentiable and to have non-null classic-curvature calculated at the origin (0, 0) of the pixel coordinate system. The theoretical basis of this research is called intensity-curvature concept. The concept envisions to replace signal intensity with the product between signal intensity and sum of second order partial derivatives of the model function. Extrapolation of the concept in two-dimensions (2D) makes it possible to calculate the ICF of an image. Theoretical treatise is presented to demonstrate the hypothesis that ICF is HPF signal. Empirical evidence then validates the assumption and also extends the comparison between ICF-based HPF and ten different HPFs among which is traditional HPF and particle swarm optimization (PSO) based HPF. Through comparison of image space and k-space magnitude, results indicate that HPFs behave differently. Traditional HPF filtering and ICF-based filtering are superior to PSO-based filtering. Images filtered with traditional HPF are sharper than images filtered with ICF-based filter. The contribution of this research can be summarized as follows: (1) Math description of the constraints that ICF need to obey to in order to function as HPF; (2) Math of ICF-based HPF of bivariate cubic B-spline; (3) Image space comparisons between HPFs; (4) K-space magnitude comparisons between HPFs. This research provides confirmation on the math procedure to use in order to design 2D HPF from a model bivariate polynomial function.

中文翻译：

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二元三次B样条模型多项式函数的基于曲率函数的数字高通滤波器

这项研究致力于基于强度曲率功能（ICF）的数字高通滤波器（HPF）的设计。ICF由双变量三次B样条模型多项式函数计算得出，称为基于ICF的HPF。为了计算ICF，模型函数需要是二阶可微的，并且必须具有在像素坐标系的原点（0，0）上计算的非零经典曲率。这项研究的理论基础称为强度-曲率概念。该概念设想用信号强度和模型函数的二阶偏导数之和之间的乘积来代替信号强度。二维（2D）概念的外推法可以计算图像的ICF。提出理论论文来证明ICF是HPF信号的假设。然后，经验证据证实了这一假设，并扩展了基于ICF的HPF与十种不同的HPF之间的比较，其中包括传统的HPF和基于粒子群优化（PSO）的HPF。通过比较图像空间和k空间大小，结果表明HPF的行为有所不同。传统的HPF过滤和基于ICF的过滤优于基于PSO的过滤。使用传统HPF过滤的图像比使用基于ICF的过滤器过滤的图像更清晰。这项研究的贡献可以归纳如下：（1）ICF作为HPF所必须遵守的约束条件的数学描述；（2）基于ICF的双变量三次B样条的数学计算；（3）HPF之间的图像空间比较；（4）HPF之间的K空间大小比较。