英語翻譯
4.THE WAVELET TRANSFORM
In this paper,the wavelet transform is utilized to determine the location of ejector pins after executing the optimization Thus,a brief description will be given of the basics of the wavelet transform in relation to the proposed problem Wavelets [11.lg] are mathematical tools for hierarchically decomposing functions.Wavelets are classified into the Haar wavelet.spline wavelet.Daubechies wavelet,etc..depending upon the basis function The simplest form of wavelet.the Haar basis,was used.One-dimensional wavelet transforms will be explained first,and it will be shown how these tools can be used to compress the representalion of a piecewise-constant function.
4.1 one-dimensional Haar wavelet transform
The Haar basis is the simplest wavelet basis To begin with.an examination will be made of how a one dimensional function can be decomposed using Haar wavelets.The algorithm will be described later.To give a brief idea of how the wavelet works,a simple example will be examined.Take a one-dimensional image with a resolution of 4 pixels [9735] This image can be represented in the Haut basis by computing the wavelet transform as follows Start by averaging,and then a new tower-resolution image is obtained with the pixel values [84].Clearly.some information has been lost in this averaging and down-sampling process In order to recover the original Bur pixel values from the two averaged pixels,it is necessary to store some detail coefficients that capture that missing information.In the present example,I will be chosen for the first detail coefficient,since the average g that was computed is 1
less than 9 and I more than 7.This single number makes it possible ed recover the first two pixels of our original four-pixel image Similarly.the second detail coefficient is - 1,since 4 + (- 1 ) - 3 and 4 - (- 1)= 5.
Summarizing.the original image has so far been decomposed into a lower-resolution version and detail coefficients as shown in Fig 4 Thus.using the onedimensional Haar basis,the wavelet transform of the original four-pixel image is given as in Fig 4.
Given the transform,it is possible to reconstruct the image to any resolution by recursively adding end subtracting the detail coefficients from the lower-resolution versions This reconstruction process is.called synthesis from decomposed images One advantage of the wavelet transform is that the characteristic representation of the original image can be obtained though synthesis Figure 5 shows the sequence of decreasing resolution approximation.