图形图像处理(第十一讲)

小波变换DWT 小波变换DWT
[CA,CD] = DWT(X,Lo_D,Hi_D) computes the wavelet decomposition as above given these filters as input: Lo_D is the decomposition low-pass lowfilter. Hi_D is the decomposition high-pass highfilter. Lo_D and Hi_D must be the same length.
DWT
Let LX = length(X) and LF = the length of filters; then length(CA) = length(CD) = LA where LA = CEIL(LX/2), if the DWT extension mode is set to periodization. LA = FLOOR((LX+LF-1)/2) for the other extension FLOOR((LX+LFmodes. For the different signal extension modes, see DWTMODE. [CA,CD] = DWT(...,'mode',MODE) computes the wavelet decomposition with the extension mode MODE you specify. MODE is a string containing the extension mode.
DWT示例 DWT示例
>>x = [1 1 0 0 1 1 0 0]; [ca,cd] = dwt(x,'db1','mode','sym')
ca =1.4142 0 1.4142 0
cd =
0
0
0
0
DWT示例 DWT示例
>> x=[1 0 1 0 1 0 1 0]; >> [ca,cd] = dwt(x,'haar','mode','sym') ca =0.7071 0.7071 0.7071 0.7071 cd = 0.7071 0.7071 0.7071 0.7071
DWT2
DWT2 Single-level discrete 2-D wavelet transform. DWT2 performs a single-level 2-D wavelet decomposition with respect to either a particular wavelet ('wname', see WFILTERS for more information) or particular wavelet filters (Lo_D and Hi_D) you specify. [CA,CH,CV,CD] = DWT2(X,'wname') computes the approximation coefficients matrix CA and details coefficients matrices CH, CV, CD, obtained by a wavelet decomposition of the input matrix X. 'wname' is a string containing the wavelet name.
DWT示例 DWT示例
[F1,F2] = WFILTERS('haar','l') F1 = 0.7071 0.7071 F2 = 0.7071 0.7071
WFILTERS
WFILTERS Wavelet filters. [LO_D,HI_D,LO_R,HI_R] = WFILTERS('wname') computes four filters associated with the orthogonal or biorthogonal wavelet named in the string 'wname'. The four output filters are: LO_D, the decomposition low-pass filter HI_D, the decomposition high-pass filter LO_R, the reconstruction low-pass filter HI_R, the reconstruction high-pass filter
WAVEDEC
N must be a strictly positive integer (see WMAXLEV). The output decomposition structure contains the wavelet decomposition vector C and the bookkeeping vector L. For [C,L] = WAVEDEC(X,N,Lo_D,Hi_D), Lo_D is the decomposition low-pass filter and Hi_D is the decomposition high-pass filter.
Biorthogonal:
'bior1.1', 'bior1.3' , 'bior1.5' 'bior2.2', 'bior2.4' , 'bior2.6', 'bior3.1', 'bior3.3' , 'bior3.5', 'bior3.9', 'bior4.4' , 'bior5.5', Reverse Biorthogonal: 'rbio1.1', 'rbio1.3' , 'rbio1.5' 'rbio2.2', 'rbio2.4' , 'rbio2.6', 'rbio3.1', 'rbio3.3' , 'rbio3.5', 'rbio3.9', 'rbio4.4' , 'rbio5.5', 'bior2.8' 'bior3.7' 'bior6.8'.
WFILTERS
Available wavelet names 'wname' are:
Daubechies: 'db1' or 'haar', 'db2', ... ,'db45' Coiflets : 'coif1', ... , 'coif5' Symlets : 'sym2' , ... , 'sym8', ... ,'sym45' Discrete Meyer wavelet: 'dmey'
小波变换DWT 小波变换DWT
[CA,CD] = DWT(X,'wname') computes the approximation coefficients vector CA and detail coefficients vector CD, obtained by a wavelet decomposition of the vector X. 'wname' is a string containing the wavelet name.
WAVEDEC
The structure is organized as: C = [app. coef.(N)|det. coef.(N)|... |det. coef.(1)] L(1) = length of app. coef.(N) L(i) = length of det. coef.(N-i+2) for i = 2,...,N+1 L(N+2) = length(X). See also dwt, waveinfo, waverec, wfilters, wmaxlev. Reference page in Help browser
Hale Waihona Puke dwt2NOTE: When X represents an indexed image, then X as well as the output arrays CA, CH, CV, CD are m-by-n matrices. When X represents a truecolor image, then they become m-by-n-by-3 arrays. These arrays consist of three m-by-n matrices (representing the red, green, and blue color planes) concatenated along the third dimension. For more information on image formats, see the reference pages of IMAGE and IMFINFO functions. Example: x = magic(4); [ca,ch,cv,cd] = dwt2(x,'db1','mode','sym') See also dwtmode, idwt2, wavedec2, waveinfo waveinfo.