Wavelet image scattering

Use the `waveletScattering2`

object to create a framework for a
wavelet image scattering decomposition using complex-valued 2-D Morlet
wavelets.

`sf = waveletScattering2`

`sf = waveletScattering2(Name,Value)`

creates a framework
for a wavelet image scattering decomposition with two complex-valued 2-D Morlet filter
banks and isotropic scale invariance. Both filter banks have quality factors of one
wavelet per octave. There are six rotations linearly spaced between 0 and π radians for
each wavelet filter. By default, `sf`

= waveletScattering2`waveletScattering2`

assumes an image
input size of 128-by-128. The scale invariance is 64.

creates a framework for wavelet image scattering with properties specified by one or more
`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 (`" "`

).

With the exceptions of `OptimizePath`

and
`OversamplingFactor`

, you cannot change a property value of an
existing scattering framework. For example, if you create a framework
`sf`

with `ImageSize`

set to ```
[256
256]
```

, you cannot assign a different `ImageSize`

to
`sf`

.

`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 |

`coefficientSize` | Size of image scattering coefficients |

`numorders` | Number of scattering orders |

`numfilterbanks` | Number of scattering filter banks |

`paths` | Scattering paths |

[1] Bruna, A., 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.