A Snake-Based Approach to Accurate Determination of Both Contact Points and Contact Angles

We present a new method based on B-spline snakes (active contours) for measuring high-accuracy contact angles. In this approach, we avoid making physical assumptions by defining the contour of the drop as a versatile B-spline curve. When useful, we extend this curve by mirror symmetry so that we can take advantage of the reflection of the drop onto the substrate to detect the position of the contact points. To keep a wide range of applicability, we refrain from discretizing the contour of the drop, and we choose to optimize an advanced image-energy term to drive the evolution of the curve. This term has directional gradient and region-based components; additionally, another term—an internal energy—is responsible for the snake elasticity and constrains the parameterization of the spline. While preserving precision at the contact points, we limit the computational complexity by constraining a non-uniform repartition of the control points. The elasticity property of the snake links the local nature of the contact angle to the global contour of the drop. A global knowledge of the drop contour allows us to use the reflection of the drop on the substrate to automatically and precisely detect a line of contact points (vertical position and tilt). We apply cubic-spline interpolation over the image of the drop; then, the evolution procedure takes part in this continuous domain to avoid the inaccuracies introduced by pixelization and discretization. We have programmed our method as a Java software and we make it freely available. Our experiments result in good accuracy thanks to our high-quality image-interpolation model, while they show applicability to a variety of images thanks to our advanced image-energy term.