Medical image processing is one of the most challenging tasks in computer vision. Many obstacles are encountered when performing automatic lesion segmentation in medical images, such as: shadows, artifacts, image quality, etc. This work aims to automatically segment a variety of medical images, overcoming all such drawbacks. To achieve this goal, we propose a combination of two convolutional neural networks and a deformable model using the spline approximation functions. More specifically, we introduce an automatic parametric active contour method based on an energy functional that combines the auto-encoder model for texture feature analysis and the U-net model for edge feature localization and extraction. The robustness of the proposed deep snake model is evaluated using three different datasets of brain MRI images, breast ultrasound images, and Foot Ulcer Segmentation Challenge 2021. Obtained results confirm that our proposed model improves segmentation performance and is robust to medical image segmentation challenges.