Quantization error in regular grids: Triangular pixels

作     者：Kamgar-Parsi, B Kamgar-Parsi, B 

作者机构：USN Res Lab Navy Ctr Appl Res Artificial Intelligence Washington DC 20375 USA USN Res Lab Div Informat Technol Washington DC 20375 USA 

出 版 物：《IEEE TRANSACTIONS ON IMAGE PROCESSING》 (IEEE Trans Image Process)

年 卷 期：1998年第7卷第10期

页      面：1496-1500页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：quantization error spatial quantization triangular pixels 2-D regular grids 

摘      要：Quantization of the image plane into pixels results in the loss of the trite location of features within pixels and introduces an error in ang quantity computed from feature positions in the image. Here, we derive closed-form, analytic expressions for the error distribution function, thr mean absolute error (MAE), and the mean square error (MSE) due to triangular tessellation, for differentiable functions of an arbitrary number of independently quantized points, using a linear approximation of the function. These quantities are essential in examining the intrinsic sensitivity of image professing algorithms. Square and hexagonal pixels were treated in previous papers. An interesting result is that for all possible cases 0.99 (D) over bar(T)/(D) over bar(S) 1.13, where (D) over bar(T) and (D) over bar(S) are the MAE in triangular and square tessellations.