A method for generating temporally stable hash values reduces visual artifacts associated with stochastic sampling of data for graphics applications. A given hash value can be generated from a scaled and discretized object-space for a geometric object within a scene. Through appropriate scaling, the hash value can be discretized and remain constant within a threshold distance from a pixel center. As the geometric object moves within the scene, a hash value associated with a given feature of the geometric object remains constant because the hash value is generated using an object-space coordinate anchored to the feature. In one embodiment, alpha testing threshold values are assigned random, but temporally stable hash output values generated using object-space coordinate positions for primitive fragments undergoing alpha testing. Alpha tested fragments are temporally stable, beneficially improving image quality.