All-or-nothing and skeleton transformation

The transformations described in the previous sections are all based on the same principle in the binary case: they examine whether a certain configuration of points (defined by the structuring element) verifies a relationship with the object under study. The all-or-nothing transformation consists in examining configurations where some points verify a relationship with the object and others verify a relationship with the object's complementary, and thus enables a fine-tuned analysis of each point's neighborhood. It should be noted, however, that this takes us outside the framework of increasing operations. The structuring elements T considered in this transformation are decomposed into T ₁ and T ₂ , which form a partition (