New algorithms for contrast enhancement in grayscale images based on the variational definition of histogram equalization

Images captured in dark or bright environments are usually characterized of low contrast. It is important to preprocess these images to make them suitable for other image processing applications. The histogram equalization (HE) algorithm is widely used for this purpose due to its simplicity and effectiveness. However, it can result in a significant change in the mean brightness and produce undesirable visual artifacts. This paper introduces the Constrained Variational Histogram Equalization (CVHE) algorithm which basically extends the variational definition of the HE algorithm by adding a mean brightness constraint to formulate a functional optimization problem, the solution of which defines a new graylevel transformation function for contrast enhancement. Preserving the mean brightness is expected to add more control on histogram stretching, thus reducing the artifacts and change in brightness. We also develop two variants of the CVHE algorithm. The first variant is the Constrained Variational Local Histogram Equalization (CVLHE) algorithm which works in a similar manner to the popular local histogram equalization (LHE) algorithm; however it uses the CVHE transformation function. This variant achieves better performance than the CVHE algorithm but with higher computational requirements. The second variant is the Accelerated CVLHE (ACVLHE) algorithm which uses a modified nonoverlapped block processing approach to reduce the CVLHE computations. The ACVLHE strikes a balance between the speed of the CVHE and the performance of the CVLHE. The choice between the CVHE algorithm and its two local variants is a tradeoff between speed and desired enhancement levels. Visual and quantitative evaluation involving benchmark images show our algorithms to be better than their HE counterparts.