A new local image processing algorithm, the Tahir algorithm, is an adaptation to the standard low-pass filter. Its design is for images that have the spectrum of pixel intensity concentrated at the lower end of the intensity spectrum. Window memoization is a specialization of memoization. Memoization is a technique to reduce computational redundancy by skipping redundant calculations and storing results in memory. An adaptation for window memozation is developed based on improved symbol generation and a new eviction policy. On implementation, the mean lower-bound speed-up achieved was between 0.32 (slowdown of approximately 3) and 3.70 with a peak of 4.86. Lower-bound speed-up is established by accounting for the time to create and delete the cache. Window memoization was applied to: the convolution technique, Trajkovic corner detection algorithm and the Tahir algorithm. Window memoization can be evaluated by calculating both the speed-up achieved and the error introduced to the output image.