waveletScattering2
Wavelet image scattering
Description
Use the waveletScattering2 object to create a network for a
wavelet image scattering decomposition using complex-valued 2-D Morlet
wavelets.
Creation
Description
sf = waveletScattering2waveletScattering2 assumes an image
input size of 128-by-128. The scale invariance is 64.
sf = waveletScattering2(Name,Value)Name,Value pair arguments. Properties can be specified in any order
as Name1,Value1,...,NameN,ValueN. Enclose each property name in single
quotes (' ') or double quotes (" ").
Note
With the exceptions of OptimizePath and
OversamplingFactor, you cannot change a property value of an
existing scattering network. For example, if you create a network
sf with ImageSize set to [256
256], you cannot assign a different ImageSize to
sf.
Properties
Object Functions
scatteringTransform | Wavelet 2-D scattering transform |
featureMatrix | Image scattering feature matrix |
log | Natural logarithm of 2-D scattering transform |
filterbank | Wavelet and scaling filters |
littlewoodPaleySum | Littlewood-Paley sum for 2-D wavelet scattering network |
coefficientSize | Size of image scattering coefficients |
numorders | Number of orders in wavelet image scattering network |
numfilterbanks | Number of filter banks in wavelet image scattering network |
paths | Scattering paths |
Examples
Create a wavelet image scattering network with default settings. The default image size is 128-by-128, and the default invariance scale is 64.
sf = waveletScattering2
sf =
waveletScattering2 with properties:
ImageSize: [128 128]
InvarianceScale: 64
NumRotations: [6 6]
QualityFactors: [1 1]
Precision: 'single'
OversamplingFactor: 0
OptimizePath: 1
Use the filterbank function to obtain the Fourier transform of the scaling function, the wavelet filters, and the center spatial frequencies of the wavelet filters.
[phif,psif,f] = filterbank(sf);
The invariance scale gives the width in the x- and y-directions of the 2-D Gaussian scaling function. To confirm the scaling function has the expected spatial width, first take the inverse Fourier transform of phif. Use the helper function helperPlotPhiSurface to plot the scaling function with the extent of the invariance scale in both x and y designated. The source code for helperPlotPhiSurface is provided in the appendix at the end of this example.
phi = ifftshift(ifft2(phif)); figure helperPlotPhiSurface(sf,phi)
The scaling function is larger than 128-by-128 because it has been padded to avoid edge effects.
Extract the Fourier transform of the coarsest scale wavelet in the second filter bank and take its inverse Fourier transform. Use helperPlotPsiSurface to plot the real and imaginary parts of the wavelet and confirm the spatial extent of the coarsest scale wavelet does not exceed the invariance scale. Similar to the scaling function, the wavelet has been padded to avoid edge effects. The source code for helperPlotPsiSurface is provided in the appendix at the end of this example.
psiF = psif{2}(:,:,end);
psiL = ifftshift(ifft2(psiF));
figure
helperPlotPsiSurface(sf,psiL)
Appendix
The following helper functions are used in this example.
helperPlotPhiSurface
function helperPlotPhiSurface(scatFrame,data) halfscale = scatFrame.InvarianceScale/2; surf(data) shading interp view(-20,35) Ysize = size(data,1); Xsize = size(data,2); Ycenter = Ysize/2; Xcenter = Xsize/2; hold on plot([Xcenter-halfscale Xcenter-halfscale],[0 Ysize], ... 'r','LineWidth',2); plot([Xcenter+halfscale Xcenter+halfscale],[0 Ysize], ... 'r','LineWidth',2); plot([0 Xsize],[Ycenter-halfscale Ycenter-halfscale], ... 'r','LineWidth',2); plot([0 Xsize],[Ycenter+halfscale Ycenter+halfscale], ... 'r','LineWidth',2); title('$\phi(x,y)$','FontSize',14,'Interpreter','Latex'); xlabel('$x$','FontSize',14,'Interpreter','Latex') ylabel('$y$','FontSize',14,'Interpreter','Latex') end
helperPlotPsiSurface
function helperPlotPsiSurface(scatFrame,data) halfscale = scatFrame.InvarianceScale/2; Ysize = size(data,1); Xsize = size(data,2); Ycenter = Ysize/2; Xcenter = Xsize/2; surf(real(data)) shading interp view(-5,13) hold on surf(imag(data)) shading interp plot([Xcenter-halfscale Xcenter-halfscale],[0 Ysize], ... 'r','LineWidth',2); plot([Xcenter+halfscale Xcenter+halfscale],[0 Ysize], ... 'r','LineWidth',2); plot([0 Xsize],[Ycenter-halfscale Ycenter-halfscale], ... 'r','LineWidth',2); plot([0 Xsize],[Ycenter+halfscale Ycenter+halfscale], ... 'r','LineWidth',2); title('$\frac{1}{2^{2J}}\psi(x/2^J,y/2^J)$','FontSize',14,... 'Interpreter','Latex'); xlabel('$x$','FontSize',14,'Interpreter','Latex') ylabel('$y$','FontSize',14,'Interpreter','Latex') view(-10,51) end
References
[1] Bruna, J., and S. Mallat. "Invariant Scattering Convolution Networks." IEEE Transactions on Pattern Analysis and Machine Intelligence. Vol. 35, Number 8, 2013, pp. 1872–1886.
[2] Sifre, L., and S. Mallat. "Rigid-Motion Scattering for Texture Classification". arXiv preprint. 2014, pp. 1–19. https://arxiv.org/abs/1403.1687.
[3] Sifre, L., and S. Mallat. "Rotation, scaling and deformation invariant scattering for texture discrimination." 2013 IEEE Conference on Computer Vision and Pattern Recognition. 2013, pp 1233–1240.
