| Variational Snake Theory (2002) | |||||||||||||||
Abstract | |||||||||||||||
| In this chapter, we review briey the theory of edge detection and its non local version, the \snake", or \active contour" theory. The snakes are curves minimizing locally a contrast and smoothness energy in the image. We show that simpler and simpler models have emerged and we support the idea that a very recent class of models proposed by Kimmel and Bruckstein is actually optimal. The snake energy simply is an average contrast across the curve, the contrast being measured as a function g of the image gradient through the snake, un . We discuss, however, this last model from two points of views : the shape of the contrast function g and the experimental blunders due to the varying contrast along the sought for boundary. This leads us to propose a very particular form of the contrast function in the mentioned snake model, as close as possible to a threshold function of the gradient. Eventually, we show by arguments and experiments that the resulting snakes simply coincide with the well contrasted level lines of the image. This is shown in two ways : rst, we prove that all meaningful level lines of the image hardly move by the snake evolution equation and second that if we evolve snakes by their energy, they tend to follow well contrasted level lines. For a sake of completeness, we give all formal computations needed for deriving the main models, their evolution equation and steady state equation. Also, the very simple direct curve energy minimization which we use for experiments is described. It does not actually use the \level set method" of Osher and Sethian. Indeed, the big claimed advantage of these methods is to deal with topology changes of the snake during the minimization process. If, as we sustain, the snakes can be replaced in most pra... | |||||||||||||||
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