Seed selection process

• To speed up the image segmentation process, the FMMIS does not use all the pixels from the image analysed. Instead, it only uses a few input pixels called seeds, to grow the hyperboxes.

• The seeds are automatically determined (located) by an ad-hoc procedure, since this process is problem-dependent.

• Considering the great variability of colour of the wood boards, the seed selection is based on adaptive thresholding in the RGB colour space.

input patterns

• The input patterns are the spatial coordinates of the seeds, with each dimension normalized in the range [0,1].

• Let X be a S x 2 input matrix, where S is the number of seeds selected

• The position of the h^th seed in the image is represented by the vector X_h = (x_h1,x_h2), where the first coordinate indicates the column and the second coordinate the row of the image.

Fuzzy min-max neural network for image segmentation (FMMIS)

• The FMMIS method places hyperboxes defined in the 2D geometric space by pairs of min-max points for each spatial coordinate of the image (rectangular boxes in the case of 2D images).
• Each hyperbox fuzzy set has an associated membership function that describes the degree of membership (spatial proximity) of a given pixel to a hyperbox in the [0,1] interval.
• When an input pattern (new seed) is presented, the hyperbox with the highest degree of membership is found and expanded to enclose the input pattern.
• The hyperbox expansion is accepted only if the region contained by the expanded hyperbox is similar in colour to the region enclosed by the hyperbox before the expansion. 

FMMIS learning algorithm

1. Initialisation
2. Hyperbox Expansion
3. Hyperbox Ovelap Test
4. Hyperbox Contraction
5. Fine-tuning Hyperbox Expansion
6. Hyperbox Merging

output of the fMMIS