Deformation-specific and deformation-invariant visual object recognition: pose vs. identity recognition of people and deforming objects.

When we see a human sitting down, standing up, or walking, we can recognize one of these poses independently of the individual, or we can recognize the individual person, independently of the pose. The same issues arise for deforming objects. For example, if we see a flag deformed by the wind, either blowing out or hanging languidly, we can usually recognize the flag, independently of its deformation; or we can recognize the deformation independently of the identity of the flag. We hypothesize that these types of recognition can be implemented by the primate visual system using temporo-spatial continuity as objects transform as a learning principle. In particular, we hypothesize that pose or deformation can be learned under conditions in which large numbers of different people are successively seen in the same pose, or objects in the same deformation. We also hypothesize that person-specific representations that are independent of pose, and object-specific representations that are independent of deformation and view, could be built, when individual people or objects are observed successively transforming from one pose or deformation and view to another. These hypotheses were tested in a simulation of the ventral visual system, VisNet, that uses temporal continuity, implemented in a synaptic learning rule with a short-term memory trace of previous neuronal activity, to learn invariant representations. It was found that depending on the statistics of the visual input, either pose-specific or deformation-specific representations could be built that were invariant with respect to individual and view; or that identity-specific representations could be built that were invariant with respect to pose or deformation and view. We propose that this is how pose-specific and pose-invariant, and deformation-specific and deformation-invariant, perceptual representations are built in the brain.

1. Introduction

When we see a human sitting down, standing up, or walking, we can recognize one of these poses independently of the individual, or we can recognize the individual person, independently of the pose. How might this be achieved in the visual system? Might both types of encoding of visual stimuli be present simultaneously, in different cortical areas? What mechanisms in the visual cortex might be involved?

The same issues arise for deforming objects. If we see a flag deformed by the wind, either blowing out or hanging languidly, we can usually recognize the flag, independently of its deformation. Similarly, we can describe the deformation of an object, for example the flag blowing out or hanging loosely, independently of the identity (e.g., nationality) of the flag.

In general, dealing with deformation in images is difficult for object recognition systems. For example, one approach has used part-based representations to recognize human poses (Yang et al., 2010), but this is unlikely to work for many objects, such as a deforming flag, and relies on accurate recognition of every part, and processing of how the parts are related to each other (Rolls, 2008).

Here we formulate a hypothesis about how the primate including human visual system may be able to implement pose recognition independently with respect to identity; and identity independently of pose, and then test the hypotheses by simulations of a model of the ventral visual cortical pathways, VisNet (Wallis and Rolls, 1997; Rolls and Milward, 2000; Rolls, 2008, 2012).

The hypothesis is that these types of recognition can be implemented by the primate visual system using the temporo-spatial continuity that we hypothesize enables transform invariant representations of objects to be learned. In particular, one hypothesis is that pose identification could be learned under conditions in which large numbers of different people are seen in the same pose, for example sitting down. As different individuals in a sitting crowd are successively fixated and used as input to the ventral visual system, the temporal continuity will be for the pose and not for the individual person, allowing pose-specific representations to be built that are independent (invariant with respect to) person identity. On another occasion, most of the people successively viewed might be standing up, for example waiting in a bus queue. On another occasion, all the individuals successively fixated might be walking to work. The second hypothesis is that person-specific representations that are independent of pose could be built, in another part of the ventral cortical visual system, when we watch one individual change posture, for example sitting down, then standing up, and then walking. The representation of the identity of another person that is invariant with respect to pose and view could be built using the temporal continuity inherent is seeing another particular person transform through a set of poses and views, etc.

These hypotheses were tested in a simulation of the ventral visual system, VisNet, that uses temporal continuity, implemented in a synaptic learning rule with a short-term memory trace of previous neuronal activity, to learn invariant representations (Rolls, 2012).

2. Methods

2.1. Experimental design

The stimuli for the human pose experiment consisted of three individuals (man, woman, and soldier), shown in each of three different poses (standing, sitting, and walking). Each image was shown in 12 different rotational views each 30° apart. To train for pose identification, during training all 36 images had the same pose in succession but with the 36 images otherwise presented in random permuted sequence. One training epoch consisted of showing successively all people and views of one pose, then all people and views of another pose, and then all identities and views of the third pose. This enabled us to test whether VisNet under these circumstances would allocate some neurons to one pose independently of individual and view, other neurons invariantly to the second pose, and other neurons invariantly to the third pose.

To train for recognition of each individual, a training epoch consisted of showing all poses and all views of one individual in a random sequence, then all poses and all views of the second individual in a random sequence, and then all poses and all views of the third individual in a random sequence. This enabled us to test whether VisNet under these circumstances would allocate some neurons to one individual person independently of pose, other neurons to the second individual independently of pose, and other neurons to the third individual. It may be emphasized that the images shown in each of these experiments were identical, and only the order in which they were presented differed.

After training, the trained networks were then tested to determine whether the poses could be identified independently of the person and view transforms; or whether the individual people could be identified independently of the pose and view transforms.

For the flag deformation experiment, there were flags of four individual countries (Holland, Spain, UK, and USA) each shown with five different deformations produced by equally spaced wind values, with each condition shown in two views, from one side, and from the other side. To train to identify the country of the flag, all the deformations and views of the flag of one country were shown in random sequence, then all the transforms of the flag of the second country, etc. To train to identify the deformation (how much the flag drooped because of different wind strengths), one deformation was trained with all images of that deformation, then all images of the second deformation, etc.

After training, the trained networks were then tested to determine whether the particular deformations of the flags produced by each wind speed could be identified independently of the country and view transforms of the flags; or whether the individual countries of each flag image could be identified independently of the deformation produced by the different wind speeds and views.

2.2. Stimulus creation

The images of humans used for training were rendered using Blender software (www.blender.org) to ensure uniform lighting conditions. The models used for rendering were generated from the MakeHuman software (www.makehuman.org). Each model was posed in three variations (standing, sitting, and walking) inside Blender. The camera position in Blender was rotated around each model in 30° increments to produce 12 views of each model in each pose, as illustrated in Figure 1. After rendering, each image was converted and scaled to an 8-bit (range: 0–255) grayscale representation, and the pixel intensities were controlled so that the mean value of each model in the front facing standing position was 127. Rendered images were placed on uniform 127 grayscale backgrounds.

Figure 1

Different views of human stimuli used to train the VisNet model. Each row shows each stimuli in one of three different poses (sitting, standing, and walking) varying across view rotation. The 12 rotations are shown, starting with 0° on the left and proceeding in 30° increments.

The images of flags for different countries (Holland, Spain, UK, and USA) were also created in Blender using its cloth simulation. A force field was placed laterally from the position of the flag to give it a fluttering motion from wind. The wind force was set to five different equally spaced values in the range 0–200 Blender units, chosen so to give a wind effect varying from no wind to strong wind. Images were rendered with the camera looking straight on to the flag and on the opposite side, as illustrated in Figure 2. Rendered images were placed on uniform 127 grayscale backgrounds.

Figure 2

The flag stimuli used to train VisNet. Each flag is shown with different wind forces and rotations. Starting on the left the first pair, both the 0° and 180° views are shown for windspeed 0, and each successive pair is shown for wind force increased by 50 blender units.

2.3. Training

Training images were presented at the center of the VisNet retina in one of two modes, object or deformation recognition mode. These modes were made distinct so that we could measure either how well the VisNet architecture performs in recognizing stimulus identity (i.e., which person it was) invariantly with respect to deformation and view; and deformation (i.e., which pose it was) invariantly with respect to stimulus identity and view.

In object recognition mode each of the images was grouped depending on the model (man, woman, and soldier for the human objects; or country for the flag objects). Each of the image groups then had each model shown in the 3 different deformations, with 12 rotational views of each deformation. During each epoch of training, using the trace synaptic learning rule, a randomly ordered permutation of the set of all images corresponding to different deformations and views was presented to VisNet. After each group of deformations and views was presented for a single model, the trace values reflecting for each neuron its recent firing rate was reset to 0 before moving on to the next model. (Trace reset speeds learning in VisNet, but is not essential for its operation Rolls and Milward, 2000; Rolls, 2012).

In deformation learning mode the images were grouped based on the different deformations (sitting, standing, and walking poses as the groups for the human objects; or wind speed deformation for the flag objects). For the pose learning of people, each training group consisted of the images of the 3 people in 12 different rotations in the same deformation. Trace learning operated in a similar fashion as above with the trace being reset after each set of a particular pose or deformation.

Simulations were run using 50 training epochs, which was sufficient to enable convergence of the synaptic weights.

2.4. Overview of the VisNet architecture

Fundamental elements of Rolls' 1992 theory for how cortical networks might implement invariant object recognition are described in detail elsewhere (Rolls, 2008, 2012). They provide the basis for the design of VisNet, which is described in the Appendix, and can be summarized as:

A series of competitive networks, organized in hierarchical layers, exhibiting mutual inhibition over a short range within each layer. These networks allow combinations of features or inputs occurring in a given spatial arrangement to be learned by neurons using competitive learning (Rolls, 2008), ensuring that higher order spatial properties of the input stimuli are represented in the network. In VisNet, layer 1 corresponds to V2, layer 2 to V4, layer 3 to posterior inferior temporal visual cortex, and layer 4 to anterior inferior temporal cortex. Layer one is preceded by a simulation of the Gabor-like receptive fields of V1 neurons produced by each image presented to VisNet (Rolls, 2012).

A convergent series of connections from a localized population of neurons in the preceding layer to each neuron of the following layer, thus allowing the receptive field size of neurons to increase through the visual processing areas or layers, as illustrated in Figure 3.

Figure 3

Convergence in the visual system. Right—as it occurs in the brain. V1, visual cortex area V1; TEO, posterior inferior temporal cortex; TE, inferior temporal cortex (IT). Left—as implemented in VisNet. Convergence through the network is designed to provide fourth layer neurons with information from across the entire input retina.

A modified associative (Hebb-like) learning rule incorporating a temporal trace of each neuron's previous activity, which, it is suggested (Földiák, 1991; Rolls, 1992, 2012; Wallis et al., 1993; Wallis and Rolls, 1997; Rolls and Milward, 2000), will enable the neurons to learn transform invariances.

2.5. Information measures of performance

The performance of VisNet was measured by Shannon information-theoretic measures that are essentially identical to those used to quantify the specificity and selectiveness of the representations provided by neurons in the brain (Rolls and Milward, 2000; Rolls and Treves, 2011; Rolls, 2012). A single cell information measure indicated how much information was conveyed by a single neuron about the most effective stimulus. A multiple cell information measure indicated how much information about every stimulus was conveyed by small populations of neurons, and was used to ensure that all stimuli had some neurons conveying information about them. In the pose or deformation recognition experiments, each stimulus was defined as a particular pose or deformation with all of its identity and view transforms. In the person or object recognition experiments, each stimulus was defined as a particular person or flag with all of its pose or deformation and view transforms. Details are provided in the Appendix.

3. Results

3.1. Humans

3.1.1. Recognition of individuals independently of pose

Figure 4 shows the information measured from a network trained in object recognition mode (in this case, recognition of the individual person) using three human individuals in three different poses (deformations). There were 12 views of each individual in each of the three poses or deformations. Figure 4A shows how a typical well trained neuron, as measured by the single cell information analysis, responded to one individual in all the different poses (deformations) at different views. The neuron responded to all views of all poses of the Soldier, and to no images of the other two individuals. The single cell information was 1.59 bits, which indicates perfect selectivity with responses to all transforms of one individual, and no responses to any other individual. (1.59 bits is log2 of the number of stimuli, in this case the three different people). Figure 4B shows another neuron that responded to most views of the Woman, but to some views of the Man. The single cell information for this neuron was 1.5 bits. The single cell information for the 75 most selective cells was high, as shown in Figure 4C. The multiple cell information was measured at 1.55 bits (as shown in Figure 4D), and corresponded to 96% correct. VisNet had thus learned to recognize the individual people independently of their pose and view transforms when trained for identity. The trace rule was important in achieving this result, for when training was with a purely associative (Hebbian) learning rule (Rolls, 2012), the multiple cell information was measured at 0.42 bits and corresponded to 52% correct.

Figure 4

Information analysis of the network trained to recognize human stimuli. (A) Firing rate response of the best single cell responding to an individual, the soldier, independently of poses and views. The transforms vary fastest over views. Thus transforms 1–12 are all views of pose 1, followed by all views of pose 2, etc. (B) Firing rate response of another single cell responding to an individual, the woman, across most poses and views, and not responding to most poses and views of the two other individuals. (C) A sorted ranking of the information for the set of 25 single cells with the highest information for each stimulus. (D) The multiple cell information of the network using the set of five best cells for each stimuli.

3.1.2. Recognition of pose independently of individual

Figure 5 shows the performance of VisNet when trained in deformation recognition mode to identify the pose independently of the individual person (object) and its view. Figure 5A shows how a typical well-trained neuron, as measured by the single cell information analysis, which responded to almost all views and all individuals in one pose (sitting). The single cell information was 1.59 bits. Figure 5B shows how another neuron responded to the majority of views and individuals in another pose (standing). The single cell information was 1.5 bits. The single cell information for the 75 most selective cells was high, as shown in Figure 5C. The multiple cell information was measured at 1.55 bits (as shown in Figure 5D), and corresponded to 96% correct. VisNet had thus learned to recognize the pose independently of the identity of the person or the view when trained for pose. The trace rule was important in achieving this result, for when training was with a purely associative (Hebbian) learning rule (Rolls, 2012), the multiple cell information was measured at 0.41 bits and corresponded to 56% correct.

Figure 5

Information analysis of the network trained to recognize human poses invariantly with respect to individual and view. (A) Firing rate response of a single cell with responses to the pose of sitting almost invariantly with respect to the 3 individuals and 12 views. Transforms vary fastest over views. (B) Firing rate response of a single cell with responses to the pose of standing almost invariantly with respect to the 3 individuals and 12 views. (C) A sorted ranking of the information for the set of 25 single cells with the highest information for each pose. (D) The multiple cell information of the network using the set of five best cells for each pose.

3.2. Flag objects

3.2.1. Recognition of flag country independently of deformation (windspeed)

Figure 6 shows the information measured from a network trained in object recognition mode to recognize four different flags independently of five deformations and two views. Figure 6A shows how a typical well-trained neuron, as measured by the single cell information analysis, responded to one flag (USA) in all the different deformations in the different views, and to none of the other flags. The single cell information was 2.0 bits (i.e., log2 of the number of flag countries). The single cell information for the 100 most selective cells was 2.0 bits (perfect discrimination), as shown in Figure 6B. The multiple cell information was measured at 2.0 bits (as shown in Figure 6C), and corresponded to 100% correct. VisNet had thus learned to recognize the individual flags for each country independently of their deformation and view transforms when trained for identity.

Figure 6

Information analysis of the network trained to recognize flag countries invariantly with respect to deformation produced by different windspeeds and views. (A) Firing rate response of a single cell with responses to the USA flag invariantly with respect to the five windspeed deformations and two views. Transforms vary fastest over views. (B) A sorted ranking of the information for the set of 25 single cells with the highest information for the flag of each country. (C) The multiple cell information of the network using the set of five best cells for each pose.

3.2.2. Recognition of windspeed (deformation) independently of flag country

Figure 7 shows the analysis for a network trained in deformation recognition mode to recognize five deformations each produced by a different windspeed, but independently of flag country and view. Figure 7A shows how a typical well trained neuron, as measured by the single cell information analysis, responded to one deformation (windspeed parameter 150) in the flags of all four countries and two views, and almost not at all to any other deformation across all countries and views. The single cell information was 2.32 bits (i.e., log2 of the number of deformation types). The single cell information for many of the 125 most selective cells was 2.32 bits (perfect discrimination), as shown in Figure 7B. The multiple cell information was measured at 2.32 bits (as shown in Figure 7C), and corresponded to 100% correct. VisNet had thus learned to recognize the deformation independently of the identity of the flag or the view when trained for deformation. In this case, VisNet had learned to recognize effectively the wind speed by the deformation it produced, independently of the country and view of each flag.

Figure 7

Information analysis of the network trained to recognize flag deformation invariantly with respect to flag country (four) and views (two). (A) Firing rate response of a single cell with responses to the windspeed with deformation parameter 150 invariantly with respect to the four country flags and two views. Transforms vary fastest over views. (B) A sorted ranking of the information for the set of 25 single cells with the highest information for each of the five deformations (windspeeds). (C) The multiple cell information of the network using the set of five best cells for each deformation (windspeed).

3.3. Flag capacity

The deformation invariant recognition of flags described above was obtained with a set of four flags (each with five deformations each with two views, as illustrated in Figure 2). On that task, performance was 100% correct. We tested how well VisNet would perform when the number of different flags in the set on which VisNet was trained and tested was increased. To perform this investigation, 24 more flags were constructed (of the NATO countries, and the NATO flag), each with the same set of deformations and views illustrated in Figure 2. Four of this further set of flags are illustrated in Figure 8. For training and testing with a given number of flags, random subsets of the flags and 60 training epochs were used. As shown in Figure 9, it was found that performance remained close to 100% correct for up to eight flags. The performance with higher numbers of flags was as follows: 10 flags = 92%; 15 flags = 86%; 20 flags = 79%.

Figure 8

Four more of the set of 24 more flag stimuli used to train VisNet to test how many flags could be recognized independently of deformation (see text). Each flag is shown with different wind forces and rotations. Starting on the left the first pair, both the 0° and 180° views are shown for windspeed 0, and each successive pair is shown for wind force increased by 50 blender units.

Figure 9

Performance of the network when trained and tested in deformation invariant object recognition for different numbers of objects, in this case flags each in five deformations and two views. The set of neurons used were the five cells with the highest single cell information for each country. The mean and standard deviation of the percent correct are shown, taken from 20 trials, with each trial using a different random subset of the 28 NATO flags. In all trials, the network was trained with 60 epochs in each layer.

3.4. Pose generalization to new human stimuli

We tested the ability of VisNet to identify human poses invariantly with respect to person and with respect to view using stimuli it had not been trained with. This was thus a cross-validation assessment of pose identification. To perform the cross-validation training and testing, three more human characters were created using the same methods as described in section 2.2, so that we could perform cross-validation training and testing on the network using six different individuals. The network was set up in deformation recognition mode as described above, that is, one of the poses formed a group the images of which were presented in a permuted sequence so that the trace rule could learn about a single pose. The group of images contained all 5 training individuals in all 12 views, and these images were permuted. After one pose group had been trained within an epoch, each of the other two pose groups was trained, to complete an epoch. The three poses were, as before, sitting, standing, and walking. Trace learning operated in a similar fashion as above with the trace being reset after every group. The network was then tested with all of the views and poses of the remaining individual person, and the output of layer 4 of the network was classified using a pattern associator that had been trained with the five training poses, see section A.1.5. The 15 single cells comprised of the 5 cells with the highest single cell information for each of the three poses were used as the input for training the pattern associator, which was then tested using the firing of the same 15 cells to the poses and views of the sixth, untrained, individual, to test how well the pose of that untrained individual was identified. The cross-validation training was perform in this leave-one-out protocol, training with five objects and testing with one.

In this cross-validation investigation, VisNet was able to correctly classify a pose with 76% accuracy, where chance was 33% accuracy. These results were found to be highly significantly different from chance with p < 10−37 using a standard binomial test. The correct classification rate for the pose of different individuals was between 30% and 92%, with a standard deviation of 26%.

In a control comparison, the performance on the same task using an untrained network was 19% correct. Thus the good performance indicating pose recognition invariant with respect to the individual and view described above was only obtained when VisNet was trained to perform the pose-recognition task.

4. Discussion

The new hypothesis about how pose is learned is that spatio-temporal continuity in the synaptic training rule in a network architecture designed to incorporate many of the properties of the hierarchy of ventral visual cortical areas can allow neurons specific to a pose and invariant with respect to individual and view to be learned, when there is continuity during training in pose. This hypothesis was confirmed by the simulation results. A similar hypothesis about how deformation-specific recognition of objects invariantly with respect to the identity and view of the object could be learned using temporal continuity was also confirmed by the simulation results.

The new hypothesis about how person identity can be learned is that spatio-temporal continuity in the synaptic training rule in the same network architecture can allow neurons specific to an individual person and invariant with respect to pose and view to be learned, when there is continuity during training in the individual person being seen. This hypothesis was confirmed by the simulation results. A similar hypothesis about how individual recognition of specific objects invariantly with respect to the deformation and view of the object can be learned using temporal continuity was also confirmed by the simulation results.

In addition, it was found that the capacity of the system allowed for more objects to be recognized independently of deformation. In addition, we found that the functional architecture of VisNet allowed pose recognition to occur for untrained individual people in a cross-validation experiment, showing domain generality of pose recognition across people.

This research provides a mechanism for leaning both pose-specific and pose invariant representations in the visual cortical areas. Some evidence for pose-specific representations are the face expression selective neurons in the cortex in the anterior part of the superior temporal sulcus, which can respond to a particular face expression, independently of the individual person (Hasselmo et al., 1989a). Some evidence for individual-specific representations are the individual-selective neurons in the cortex in the gyrus of the inferior temporal visual cortex, which can respond to a particular individual, independently of the face expression (Hasselmo et al., 1989a). Further evidence for pose-specific neurons is that some neurons in the temporal visual cortical areas respond to face view (e.g., the right profile) relatively independently of the individual person (Perrett et al., 1985; Hasselmo et al., 1989b); and that other neurons respond for example to people walking (Barraclough et al., 2006).

The learning described here is made possible by use of a learning rule with a trace of previous neuronal activity, allowing neurons to learn from the temporal statistics of objects in the natural world as they transform continuously in time. We developed this hypothesis (Földiák, 1991; Rolls, 1992, 1995, 2012; Wallis et al., 1993) into a model of the ventral visual system that can account for translation, size, view, lighting, and rotation invariance (Wallis and Rolls, 1997; Rolls and Milward, 2000; Stringer and Rolls, 2000, 2002, 2008; Rolls and Stringer, 2001, 2006, 2007; Elliffe et al., 2002; Perry et al., 2006, 2010; Stringer et al., 2006, 2007; Rolls, 2008, 2012). Consistent with the hypothesis, we have demonstrated these types of invariance (and spatial frequency invariance) in the responses of neurons in the macaque inferior temporal visual cortex (Rolls et al., 1985, 1987, 2003; Rolls and Baylis, 1986; Hasselmo et al., 1989b; Tovee et al., 1994; Booth and Rolls, 1998). Moreover, we have tested the hypothesis by placing small 3D objects in the macaque's home environment, and showing that in the absence of any specific rewards being delivered, this type of visual experience in which objects can be seen from different views as they transform continuously in time to reveal different views leads to single neurons in the inferior temporal visual cortex that respond to individual objects from any one of several different views, demonstrating the development of view-invariance learning (Booth and Rolls, 1998). (In control experiments, view invariant representations were not found for objects that had not been viewed in this way). The learning shown by neurons in the inferior temporal visual cortex can take just a small number of trials (Rolls et al., 1989). The finding that temporal contiguity in the absence of reward is sufficient to lead to view invariant object representations in the inferior temporal visual cortex has been confirmed (Li and DiCarlo, 2008, 2010, 2012). The importance of temporal continuity in learning invariant representations has also been demonstrated in human psychophysics experiments (Perry et al., 2006; Wallis, 2013). Some other simulation models are also adopting the use of temporal continuity as a guiding principle for developing invariant representations by learning (Wiskott and Sejnowski, 2002; Wiskott, 2003; Wyss et al., 2006; Franzius et al., 2007), and the temporal trace learning principle has also been applied recently (Isik et al., 2012) to HMAX (Riesenhuber and Poggio, 2000; Serre et al., 2007), which nevertheless does not produce representations similar to those found in the inferior temporal visual cortex (Rolls, 2012).

The findings described in this paper demonstrate a mechanism by which neurons that respond to pose independently of individual person identity could be formed, and also how neurons that respond to identity independently of pose could be formed. The natural world conditions that could provide the appropriate conditions for these two types of representation to be formed include the following. To learn pose independently of identity the natural world might consist of large numbers of individuals all in the same pose, for example all standing up (perhaps in a queue), or all sitting down (for example in a theatre or stadium). As the eyes moved over scenes of this type, the natural environment would provide the conditions of temporal continuity for pose to be learned independently of identity. To learn identity independently of pose, appropriate environmental conditions might include looking at a single person while that person alters pose, from perhaps lying down, then sitting, and then standing up. This leads to the interesting prediction that neurons that encode pose independently of identity might be more likely to be close to parts of the temporal lobe visual cortex where the representations are of large-scale, such as scenes; whereas neurons sensitive to identity independently of pose might be more likely to be found close to cortical areas where single objects are represented, such as faces. In any case, self-organizing topological maps would be likely to be formed so that these two types of representation would be somewhat separated into different cortical regions or neuronal clusters (Rolls, 2008). Further segregation might occur because some poses such as walking are associated with movement, and thus representations of such poses might be close to the temporal lobe visual cotical areas with movement-related neurons (Baylis et al., 1987; Hasselmo et al., 1989b; Barraclough et al., 2006).

Conflict of interest statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

xj:	jth input to the neuron.	y:	Output from the neuron.
yτ:	Trace value of the output of the neuron at time step τ.	α:	Learning rate.
wj:	Synaptic weight between jth input and the neuron.	η:	Trace value. The optimal value varies with presentation sequence length.

Table A1

VisNet dimensions.

	Dimensions	# Connections	Radius
Layer 4	128 × 128	400	48
Layer 3	128 × 128	400	36
Layer 2	128 × 128	400	24
Layer 1	128 × 128	100	24
Input layer	256 × 256 × 16	–	–

Table A2

Sigmoid parameters for the runs with 25 locations by Rolls and Milward (2000).

Layer	1	2	3	4
Percentile	99.2	98	88	95
Slope β	190	40	75	26

Table A3

Lateral inhibition parameters for the 25-location runs.

Layer	1	2	3	4
Radius, σ	1.38	2.7	4.0	6.0
Contrast, δ	1.5	1.5	1.6	1.4

Table A4

VisNet layer 1 connectivity.

Frequency	0.5	0.25	0.125	0.0625
# Connections	74	19	5	2

The frequency is in cycles per pixel.