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# The 2 x 2 / 2 Fuzzy Curve Pyramid

Similar to the 2x2/2 curve pyramid, there are three step when constructing a fuzzy curve pyramid. Additionally, fuzzy criteria are introduced:
• fuzzy split - subdivision of the cell contents by introducing a diagonale.
• fuzzy transitive closure - construction of the curve relation of a cell at level n+1 out of the four triangles of level n.
• fuzzy reduce - the relation code used for processing the fuzzy transitive closure is converted to the code used by the next level.

Construction of a fuzzy curve pyramid

Properties of the 2 x 2 / 2 fuzzy curve pyramid

• length reduction property - reduction of the number of curve code elements after every reduction step (similar to the 2x2/2 curve pyramid).
• minimum strength - if a single curve intersects the receptive field of a cell at level n, the grade-membership of the relation at level n will be the minimum of the grade-memberships of the curve segments of the base level.
• maximum strength - every curve will remain connected by the fuzzy reduction process and the strength of all fuzzy curve relations derived from one curve will be greater or equal to the strength of the curve in the base of the pyramid, i.e. the strength of the curve is preserved.
• minimax principle - the strength of a curve is the minimum of the strength of its segments. Furthermore, the strength of a side of a cell in the curve pyramid has the maximum strength of all curves intersecting this side.