The human visual system has the ability to group parts of stimuli into larger, inherently structured units. In this article, a computational model inspired by tolerance space theory simulating the human perceptual grouping of dot patterns is proposed. Tolerance space theory introduces a tolerance relation to a discrete set to formulate the continuity of the discrete patterns. The model proposed herein includes one- and two-reach methods based on the assumption that dot patterns can be represented in the proposed extended tolerance space (ETS). Both methods are used to construct a ratio neighborhood graph (RANG), calculate tolerance from the diagram, compute the new RANG, and then rebuild continuous structures from the new RANG with a combinatorial procedure. Experiments are conducted to show the high consistency of the proposed model with human perception for various shapes of dot patterns, its ability to simulate Gestalt proximity and similarity principles, and its potential application in computer vision. In addition, the close relationship of the proposed model with the Pure Distance Law is comprehensively revealed, and the hierarchical representation of perceptual grouping is simulated with an adaptation of the proposed model based on the ETS.

In this article, a computational model for the proximity principle for dot-pattern grouping inspired by tolerance space theory is proposed. This model includes a one-reach method, a two-reach method, and a combination process to reconstruct the continuous structure of the dot patterns. The edge ratio sequence in the so-called diagram is investigated to find a tolerance for the ETS, which serves as a threshold for removing unreasonable edges. Experiments and quantitative evaluations on continuous structure reconstruction, proximity, similarity principle simulation, and image segmentation reveal the effectiveness of the proposed model in perceptual grouping and computer vision. The close relationship between the proposed model and the PDL is comprehensively analyzed, and the ability to adapt the proposed model to simulate distance-modulated perceptual grouping of dot patterns is discussed. Finally, the possible physiological significance and potential applications of our model have also been discussed, offering new perspectives for these research fields.