# imageset3: A simulated set of images In GET: Global Envelopes

 imageset3 R Documentation

## A simulated set of images

### Description

A simulated set of images with a categorical factor (with three levels)

### Usage

data("imageset3")

### Format

A list of the image_set containing the simulated images, and the discrete group factor in the list component Group.

### Details

We considered a categorical factor Group obtaining the values 0, 1 or 2 according to the group to which the image belongs to (10 images in each of the three groups). The images were simulated in the square window [-1,1]^2 from the general linear model (GLM)

Y(r) = exp(-10 ||r||) (1 + 1(g=2)) + e(r),

where ||r|| denotes the Euclidean distance of the pixel to the origin, g is the group and the error stems from an inhomogeneous distribution over \$I\$ with the normal and bimodal errors in the middle and periphery of the image:

e(r) = 1(||r|| <= 0.5) G(r) + 1(||r|| > 0.5) 0.5 G(r)^{1/5},

where G(r) is a Gaussian random field with the exponential correlation structure with scale parameter 0.15 and standard deviation 0.2. Consequently, the first two groups (0,1) have the same mean, while a bigger bump appears in the third group (2) in the middle of the image.

### References

Mrkvička, T., Myllymäki, M., Kuronen, M. and Narisetty, N. N. (2022) New methods for multiple testing in permutation inference for the general linear model. Statistics in Medicine 41(2), 276-297. doi: 10.1002/sim.9236

graph.fanova, frank.fanova

### Examples

data("imageset3")
plot(imageset3\$image_set, idx=c(1:5, 11:15, 21:25), ncol=5)

# Colors can be changed as follows:
plot(imageset3\$image_set, idx=c(1:5, 11:15, 21:25), ncol=5) +