Wavelet function, scaling function and discrete wavelet transform

Author(s):  
Q. Jin ◽  
K.M. Wong ◽  
Z.Q. Luo
Author(s):  
Bao Qin Wang ◽  
Gang Wang ◽  
Xiao Hui Zhou ◽  
Yu Su

In this paper, a simple method is given in order to construct an area preserving mapping from a developable surface M to a plane. Based on the area preserving projection, we give some important formulas on M, and define a multi-resolution analysis on L2(M). We provide the conditions to further discuss the continuous wavelet transform and discrete wavelet transform on developable surface. At the same time, we derived two-scale equations that the scaling function and wavelet function on developable surface satisfied, we also define and discuss the orthogonality, and several important theorems are given. Finally, we construct the numerical examples. The focus of this paper is the area preserving mapping that from developable surface M to a plane, and the discrete wavelet transform on developable surface.


Informatica ◽  
2013 ◽  
Vol 24 (4) ◽  
pp. 657-675
Author(s):  
Jonas Valantinas ◽  
Deividas Kančelkis ◽  
Rokas Valantinas ◽  
Gintarė Viščiūtė

2020 ◽  
Vol 64 (3) ◽  
pp. 30401-1-30401-14 ◽  
Author(s):  
Chih-Hsien Hsia ◽  
Ting-Yu Lin ◽  
Jen-Shiun Chiang

Abstract In recent years, the preservation of handwritten historical documents and scripts archived by digitized images has been gradually emphasized. However, the selection of different thicknesses of the paper for printing or writing is likely to make the content of the back page seep into the front page. In order to solve this, a cost-efficient document image system is proposed. In this system, the authors use Adaptive Directional Lifting-Based Discrete Wavelet Transform to transform image data from spatial domain to frequency domain and perform on high and low frequencies, respectively. For low frequencies, the authors use local threshold to remove most background information. For high frequencies, they use modified Least Mean Square training algorithm to produce a unique weighted mask and perform convolution on original frequency, respectively. Afterward, Inverse Adaptive Directional Lifting-Based Discrete Wavelet Transform is performed to reconstruct the four subband images to a resulting image with original size. Finally, a global binarization method, Otsu’s method, is applied to transform a gray scale image to a binary image as the output result. The results show that the difference in operation time of this work between a personal computer (PC) and Raspberry Pi is little. Therefore, the proposed cost-efficient document image system which performed on Raspberry Pi embedded platform has the same performance and obtains the same results as those performed on a PC.


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