VL_PLOTSS(SS) plots the scale space SS. SS is a structure with the following members:

ss.firstOctave

The index of the first octave in the scale space.

ss.lastOctave

The index of the last octave in the scale space.

ss.octaveResolution

The octave resolution, i.e. the nubmer of subdivisions per octave.

ss.octaveFirstLevel

The index of the first level of subdivisions for each octave.

ss.octaveLastLevel

The iundex of last leve of subdivisions for each cotave.

ss.data

A cell array of 3D arrays representing the scale space data. The cell array has a length equal to the nubmer of octaves contained in the scale space. Each entry is a 3D array, the first two dimensions of which correspond to image rows and columns respectively, and the third to scale levels.

ss.sigma0

Base smoothing.

A scale space is a representation of a 2D signal (image) at multiple scales. In the simplest case, a scale SIGMA is defined as the input image I(x,y) convolved by a Gaussian kernel of isotropic standard deviation SIGMA:

  I(x,y;sigma) = (g_sigma * I)(x,y)


where scales are sampled as follows:

  sigma(o,s) = sigma0 2^{o + s / ss.octaveResolution),
ss.firstOctave <= o <= ss.lastOctave,
ss.octaveFirstLeve <= s <= ss.octaveLastLevel.


Moving from one octave to the next, the size of the kernel doubles. Hence the effective bandwith of the signal halves, and resolution can be reduced by half. Typically, for example, sigma0 = 1.6, so at octave 0 the image can be effectively sampled with a step of 1, and the resolution of octave 0 is the same as the one at which the input image is presented. Then at octave o the sampling step is 2^o.

ss.octaveResolution is the number of scale subdivisions per octave. ss.firstOctave and ss.lastOctave give the additional flexibility of specifying a range for the level index s to exceed the standard setting [0, ss.octaveResolution-1]. In this manner the same scales can be represented twice, at two sampling rates. This is often convenient in feature computation (e.g. to find local maxima in scale of a function).

VL_PLOTSS(SS, 'Option', value) supports the following options:

Uniform false

If TRUE then use a fixed gray scale for all the levels.