Numerosity depends on normalized contrast energy: Review and square-root law model

Area of Science:

• Visual Perception
• Psychophysics
• Computational Neuroscience

Background:

• Perceived numerosity of visual items is influenced by display characteristics.
• Contrast energy (CE) is a key factor in how we perceive the quantity of items.

Purpose of the Study:

• To develop and validate a model explaining numerosity judgments based on contrast energy.
• To investigate the relationship between contrast energy, item count, and perceived numerosity across different tasks.

Main Methods:

• Developing a mathematical model based on the square root of contrast energy (√(CE)) normalized by contrast amplitude.
• Testing the model against empirical data from various numerosity judgment tasks.
• Analyzing numerosity discrimination thresholds and sensitivity.

Main Results:

• The √(CE) model accurately fits numerosity judgment data across a wide range of item counts (N).
• The model explains phenomena like general underestimation, contrast independence in segregated displays, and contrast-dependent illusions.
• Judged numerosity shows a linear increase with the square root of the number of items (√(N)) above the subitization range.

Conclusions:

• Normalized contrast energy is proposed as the primary sensory code for numerosity perception beyond subitization.
• The square-root law provides a robust framework for understanding numerosity judgments in vision.
• This model advances our understanding of how visual system processes quantity information.