Nowadays, most of the data obtained using image and video sensors are discrete in nature and represent mappings of continuous processes onto metric spaces with a given dimension. The discretized data can be naturally represented as point arrays on regular integer grids of the corresponding dimension. The obtained arrays of points in a given metric space can be studied from the point of view of their spatial characteristics and relations between the points of the set, which, together with the growth of the amount of data obtained, lead to the need to develop specialized geometric data structures and computer algorithms for their effective processing. The paper presents a unified approach to the processing of discrete point data, which is based on their indexing in a space of a given dimension for solving computational geometry and image processing tasks. A time-efficient bijective geometric hashing method for grid-based data and an approach to organizing interaction of indexed structures have been developed. The proposed techniques have been implemented as computer software in the Python language, and computer experiments have been conducted to assess the effectiveness of the developed approach.