Edge strength function (ESF) generates a family of level curves that evolves under the influence of curvature motions. This function is proved to be useful in representing images in computer vision for analysis and recognition purposes in different contexts. Computation of the ESF requires solving a partial differential equation, hence computationally costly. In this work, we present two parallel implementations of ESF that work on Graphics Processing Units (GPU) using Compute Unified Design Architecture (CUDA). Both implementations reduce the computational time significantly with respect to their serial counterpart. The implementations differ mainly in the type of memory that is utilized for accessing data; the first approach utilizes the shared memory and the second one utilizes the texture memory. We obtain between 40 to 65 times speedup in the shared memory based implementation and between 35 to 55 times in the texture memory based implementation with respect to the single threaded CPU implementation. The amount of speedup changes depending on the data size..