The roles of endstopped and curvature tuned computations in a hierarchical representation of 2D shape

Abstract

That shape is important for perception has been known for almost a thousand years (thanks to Alhazen in 1083) and has been a subject of study ever since by scientists and phylosophers (such as Descartes, Helmholtz or the Gestalt psychologists). Shapes are important object descriptors. If there was any remote doubt regarding the importance of shape, recent experiments have shown that intermediate areas of primate visual cortex such as V2, V4 and TEO are involved in analyzing shape features such as corners and curvatures. The primate brain appears to perform a wide variety of complex tasks by means of simple operations. These operations are applied across several layers of neurons, representing increasingly complex, abstract intermediate processing stages. Recently, new models have attempted to emulate the human visual system. However, the role of intermediate representations in the visual cortex and their importance have not been adequately studied in computational modeling.This paper proposes a model of shape-selective neurons whose shape-selectivity is achieved through intermediate layers of visual representation not previously fully explored. We hypothesize that hypercomplex--also known as endstopped--neurons play a critical role to achieve shape selectivity and show how shape-selective neurons may be modeled by integrating endstopping and curvature computations. This model--a representational and computational system for the detection of 2-dimensional object silhouettes that we term 2DSIL--provides a highly accurate fit with neural data and replicates responses from neurons in area V4 with an average of 83% accuracy. We successfully test a biologically plausible hypothesis on how to connect early representations based on Gabor or Difference of Gaussian filters and later representations closer to object categories without the need of a learning phase as in most recent models.

Figure 1. Architecture of the representational and computational system for the detection of 2-dimensional object silhouettes (2DSIL).

Figure 2. Endstopping.

(A) Model complex cell. (B) Structure of model endstopped cell. (C) Response of the model endstopped cells to different radius of curvatures. Simple cell sizes were 40 (blue color), 80 (red color), 100 (green color) and 120 pixels (black color).  = (10,20,25,30). AR (aspect ratio) = (1.15,2,3,4). WR (width ratio) = 2.5 for all cells. Gain c = (0.7,0.8,1,2). Responses were normalized for the range [0,1].

Figure 3. Model endstopped cell selective for curvature sign.

Figure 4. Shape-selective neuron.

(A) Shape-selective neurons respond to different curvatures at different positions. The response is maximal when those curvatures are present at their selective positions (red). If they are in nearby positions the neuron provides some response as well (orange and yellow). (B) Shape-selective neuron tuning profile for location and curvature. (C) Shape neuron response to different stimuli, maximum response is to the stimulus at the top (value 1).

Figure 5. Comparison to Figure 2 of .

Cells responses are on the left (© 2001 The American Physiological Society, reproduced with permission) and their respective model responses are on right.

Figure 6. Comparison to Figure 4 of .

Cells responses are on the left (© 2001 The American Physiological Society, reproduced with permission) and their respective model responses are on right.

Figure 7. Comparison to Figure 5 of .

Cells responses are on the left (© 2001 The American Physiological Society, reproduced with permission) and their respective model responses are on right.

Figure 8. Comparison to Figure 8 of .

Cells responses are on the left (© 2001 The American Physiological Society, reproduced with permission) and their respective model responses are on right.

Figure 9. Difference between the model's Shape-selective neurons and 75 real cells responses from area V4.

Figure 10. How the features for isolating a Shape neuron are obtained.

See text.