There exists extensive literature in cognitive science and psychology claiming the presence of indicators of criticality in several cognitive phenomena. However, the absence of quantitative models to understand how criticality produces the observed behavior makes it impossible to derive testable predictions. In particular, in active perception, the characterization of visual processes is frequently based only on the appearance of patterns in the analysis of experimental data without exploring their causes. Assuming a more formal viewpoint, we propose that statistical mechanics would be a general framework to connect active perception with a complex systems perspective. We show that this approach provides methods and experimental tools to measure the "thermodynamic properties" of perceptual processes in a simple visual task by identifying when a system is operating in a critical regime. Our model characterizes different perceptive modes to solve a visual illusion through thermodynamic regimes. Finally, we connect them with different perceptual strategies of exploiting directional symmetries.