Question active contour model energy function

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I have hard to understand how snake energy function.

$$E_{\mathrm{smade}}^{*}=\int_{0}^{1}E_{\mathrm{suake}}(\mathbf{v}(s)),d s=\int_{0}^{1}(E_{\mathrm{imteral}}(\mathbf{v}(s))+E_{\mathrm{image}}(\mathbf{v}(s))+E_{\mathrm{con}}(\mathbf{v}(s)))d s$$

  1. Why integral from 0 to 1? It looks like haveing n points of v. This parameterize to $v(s)$ and looks like $s$ is a unit length.

  2. If I have picture, how to transform all pixel s to $E_{image}$ term