Multi Focus Image Fusion based on Linear Combination of Images using Incremental Images

This article presents three algorithms to determinate multifocus image fusion. These algorithms are based on a linear combination of two images with different focus distances. The three algorithms maximize a linear function with spatial coherence constrains. We present these algorithms in sequence to show how we devised a fast and simple algorithm. The first algorithm, CLI (for its acronym in spanish Combinacion Lineal de Imagenes) was implemented using Wolfram Mathematica, but given the number of variables to optimize, the solution takes a lot of computing time. The second algorithm, CLI-V (for its acronym in spanish Combinacion Lineal de Imagenes por Ventanas) is an application of algorithm CLI on image regions to improve the time performance and being able to implement it through the Simplex method. The third algorithm, CLI-S (for its acronym in spanish Combinacion Lineal de Imagenes Simple), is a simplification on CLI-V. This last algorithm is much faster exhibiting results of similar quality to the previous two, with a performance comparable to the results presented in the state of the art. CLI-S was implemented using the concept of integral images. This fact allows the algorithm to produce results in hundredth of a second for the test images analized. The results of the three algorithms are compared using one set of synthetic and four sets of real images. The real images are commonly used by the state of the art proposal; they were so that the reader can make a qualitative comparison of results. The synthetic images are reconstructed with 98 % accuracy in 0.080 s. and the image size is 512 x 512, this situation allows us to say that CLI-S can be used as a real-time algorithm of multifocus image fusion and we have not found a similar proposal in the state of art.