The basic goals of this paper target on the development and implementation of algorithms which provide the energy-minimizing snakes in parametric form, then in applying them to textural analysis based medical diagnosis. In order to derive these algorithms, we focus on Finite Differences Methods (Explicit and Crank-Nicolson Finite Difference Schemes), widely used in medical image processing applications. We examine the consistency, stability, and convergence rate, proving their increased quality able to provide maximum accuracy when determining the diseased anatomic tissue delimitation in the context of medical images.