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Are v1 simple cells optimized for visual occlusions? A comparative study.

Bornschein J, Henniges M, Lücke J - PLoS Comput. Biol. (2013)

Bottom Line: Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges.We find the image encoding and receptive fields predicted by the models to differ significantly.In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of 'globular' fields well.

View Article: PubMed Central - PubMed

Affiliation: Frankfurt Institute for Advanced Studies, Goethe-Universität Frankfurt, Frankfurt, Germany.

ABSTRACT
Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of 'globular' receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of 'globular' fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of 'globular' fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of 'globular' fields well. Our computational study, therefore, suggests that 'globular' fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex.

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Related in: MedlinePlus

Decomposition of image patches into basic components for four example patches.For each example the figure shows: the original patch (left), its DoG preprocessed version (second to left), and the decomposition of the preprocessed patch by the three models. For better comparison with the original patches, basis functions are shown in grey-scale. The displayed functions correspond to the active units of the most likely hidden state given the patch. In the case of standard sparse coding, the basis functions are displayed in the order of their contributions. Standard sparse coding (SC) uses many basis functions for reconstruction but many of them contribute very little. BSC uses a much smaller subset of the basis functions for reconstruction. MCA typically uses the smallest subset. The basis functions of MCA usually correspond directly to edges or to two dimensional structures of the image while basis functions of BSC and (to a greater degree) of SC are more loosely associated with the true components of the respective patch. The bottom most example illustrates that the globular fields are usually associated with structures such as end-stopping or corners. For the displayed examples, the normalized root-mean-square reconstruction errors (nrmse) allow to quantify the reconstruction quality. For standard sparse coding the errors are (from top to bottom) given by 0.09, 0.08, 0.10 and 0.12, respectively. For the two models with Bernoulli prior they are larger with 0.51, 0.63, 0.53, and 0.42 for MCA, and 0.37, 0.47, 0.44 and 0.39 for BSC. We give reconstruction errors for completeness but note that they are for all models based on their most likely hidden states (MAP estimates). For MCA and BSC the MAP was chosen for illustrative purposes while for most tasks these models can make use of their more elaborate posterior approximations.
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pcbi-1003062-g005: Decomposition of image patches into basic components for four example patches.For each example the figure shows: the original patch (left), its DoG preprocessed version (second to left), and the decomposition of the preprocessed patch by the three models. For better comparison with the original patches, basis functions are shown in grey-scale. The displayed functions correspond to the active units of the most likely hidden state given the patch. In the case of standard sparse coding, the basis functions are displayed in the order of their contributions. Standard sparse coding (SC) uses many basis functions for reconstruction but many of them contribute very little. BSC uses a much smaller subset of the basis functions for reconstruction. MCA typically uses the smallest subset. The basis functions of MCA usually correspond directly to edges or to two dimensional structures of the image while basis functions of BSC and (to a greater degree) of SC are more loosely associated with the true components of the respective patch. The bottom most example illustrates that the globular fields are usually associated with structures such as end-stopping or corners. For the displayed examples, the normalized root-mean-square reconstruction errors (nrmse) allow to quantify the reconstruction quality. For standard sparse coding the errors are (from top to bottom) given by 0.09, 0.08, 0.10 and 0.12, respectively. For the two models with Bernoulli prior they are larger with 0.51, 0.63, 0.53, and 0.42 for MCA, and 0.37, 0.47, 0.44 and 0.39 for BSC. We give reconstruction errors for completeness but note that they are for all models based on their most likely hidden states (MAP estimates). For MCA and BSC the MAP was chosen for illustrative purposes while for most tasks these models can make use of their more elaborate posterior approximations.

Mentions: In analogy to Fig. 3 C, inferred degrees of sparsity are plotted in Fig. 4 B for different numbers of basis functions. For both models, MCA and BSC, the average number of active hidden units decreases (sparsity increases) with increasing number of basis functions (i.e., with increasing over-completeness). However, while both models converge to increasingly sparse solutions, the non-linear model was found to be consistently and very significantly sparser. On patches and hidden variables the non-linear model estimates a patch to consists of on average four to five components (basis functions) compared to seven to eight as estimated by the linear model. Fig. 5 illustrates the different encodings of the two models for different example patches. For the simple example patch showing an oriented ‘branch’ (Fig. 5, top), both models combine basis functions of similar orientation. However, MCA uses fewer ‘line segments’ to re-construct the patch while BSC uses more basis functions. For patches with more complex structures (Fig. 5, examples in the middle), the differences become still more salient. Again, MCA uses fewer basis functions and usually reconstructs a patch from components which correspond to actual components in a patch. The final example (Fig. 5, bottom) illustrates inference with Gabor-like and globular components. The MCA model uses a globular field to reconstruct a two dimensional end-stopping structure. In the example, BSC reconstructs the patch by exclusively using Gabors. Some of them are very localized but clearly Gabor-like fields (the two right-hand-side fields). Often the BSC fields are not closely aligned with true image components. Sometimes we also observed BSC to use a globular field for an end-stopping structure but it does so much more rarely than MCA. We have never observed standard sparse coding to use a globular field for the examples investigated. In general, BSC and (much more so) standard sparse coding use more basis functions (reflecting the lower sparsity) and usually combine components which do not directly correspond to actual image components. In control experiments using different preprocessing approaches, we found that concrete sparsity levels do depend on the type of preprocessing. However, as was the case for the percentage of globular fields, in all experiments sparsity levels were consistently much higher for the non-linear model than for the linear one (see Methods and SI).


Are v1 simple cells optimized for visual occlusions? A comparative study.

Bornschein J, Henniges M, Lücke J - PLoS Comput. Biol. (2013)

Decomposition of image patches into basic components for four example patches.For each example the figure shows: the original patch (left), its DoG preprocessed version (second to left), and the decomposition of the preprocessed patch by the three models. For better comparison with the original patches, basis functions are shown in grey-scale. The displayed functions correspond to the active units of the most likely hidden state given the patch. In the case of standard sparse coding, the basis functions are displayed in the order of their contributions. Standard sparse coding (SC) uses many basis functions for reconstruction but many of them contribute very little. BSC uses a much smaller subset of the basis functions for reconstruction. MCA typically uses the smallest subset. The basis functions of MCA usually correspond directly to edges or to two dimensional structures of the image while basis functions of BSC and (to a greater degree) of SC are more loosely associated with the true components of the respective patch. The bottom most example illustrates that the globular fields are usually associated with structures such as end-stopping or corners. For the displayed examples, the normalized root-mean-square reconstruction errors (nrmse) allow to quantify the reconstruction quality. For standard sparse coding the errors are (from top to bottom) given by 0.09, 0.08, 0.10 and 0.12, respectively. For the two models with Bernoulli prior they are larger with 0.51, 0.63, 0.53, and 0.42 for MCA, and 0.37, 0.47, 0.44 and 0.39 for BSC. We give reconstruction errors for completeness but note that they are for all models based on their most likely hidden states (MAP estimates). For MCA and BSC the MAP was chosen for illustrative purposes while for most tasks these models can make use of their more elaborate posterior approximations.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3675001&req=5

pcbi-1003062-g005: Decomposition of image patches into basic components for four example patches.For each example the figure shows: the original patch (left), its DoG preprocessed version (second to left), and the decomposition of the preprocessed patch by the three models. For better comparison with the original patches, basis functions are shown in grey-scale. The displayed functions correspond to the active units of the most likely hidden state given the patch. In the case of standard sparse coding, the basis functions are displayed in the order of their contributions. Standard sparse coding (SC) uses many basis functions for reconstruction but many of them contribute very little. BSC uses a much smaller subset of the basis functions for reconstruction. MCA typically uses the smallest subset. The basis functions of MCA usually correspond directly to edges or to two dimensional structures of the image while basis functions of BSC and (to a greater degree) of SC are more loosely associated with the true components of the respective patch. The bottom most example illustrates that the globular fields are usually associated with structures such as end-stopping or corners. For the displayed examples, the normalized root-mean-square reconstruction errors (nrmse) allow to quantify the reconstruction quality. For standard sparse coding the errors are (from top to bottom) given by 0.09, 0.08, 0.10 and 0.12, respectively. For the two models with Bernoulli prior they are larger with 0.51, 0.63, 0.53, and 0.42 for MCA, and 0.37, 0.47, 0.44 and 0.39 for BSC. We give reconstruction errors for completeness but note that they are for all models based on their most likely hidden states (MAP estimates). For MCA and BSC the MAP was chosen for illustrative purposes while for most tasks these models can make use of their more elaborate posterior approximations.
Mentions: In analogy to Fig. 3 C, inferred degrees of sparsity are plotted in Fig. 4 B for different numbers of basis functions. For both models, MCA and BSC, the average number of active hidden units decreases (sparsity increases) with increasing number of basis functions (i.e., with increasing over-completeness). However, while both models converge to increasingly sparse solutions, the non-linear model was found to be consistently and very significantly sparser. On patches and hidden variables the non-linear model estimates a patch to consists of on average four to five components (basis functions) compared to seven to eight as estimated by the linear model. Fig. 5 illustrates the different encodings of the two models for different example patches. For the simple example patch showing an oriented ‘branch’ (Fig. 5, top), both models combine basis functions of similar orientation. However, MCA uses fewer ‘line segments’ to re-construct the patch while BSC uses more basis functions. For patches with more complex structures (Fig. 5, examples in the middle), the differences become still more salient. Again, MCA uses fewer basis functions and usually reconstructs a patch from components which correspond to actual components in a patch. The final example (Fig. 5, bottom) illustrates inference with Gabor-like and globular components. The MCA model uses a globular field to reconstruct a two dimensional end-stopping structure. In the example, BSC reconstructs the patch by exclusively using Gabors. Some of them are very localized but clearly Gabor-like fields (the two right-hand-side fields). Often the BSC fields are not closely aligned with true image components. Sometimes we also observed BSC to use a globular field for an end-stopping structure but it does so much more rarely than MCA. We have never observed standard sparse coding to use a globular field for the examples investigated. In general, BSC and (much more so) standard sparse coding use more basis functions (reflecting the lower sparsity) and usually combine components which do not directly correspond to actual image components. In control experiments using different preprocessing approaches, we found that concrete sparsity levels do depend on the type of preprocessing. However, as was the case for the percentage of globular fields, in all experiments sparsity levels were consistently much higher for the non-linear model than for the linear one (see Methods and SI).

Bottom Line: Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges.We find the image encoding and receptive fields predicted by the models to differ significantly.In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of 'globular' fields well.

View Article: PubMed Central - PubMed

Affiliation: Frankfurt Institute for Advanced Studies, Goethe-Universität Frankfurt, Frankfurt, Germany.

ABSTRACT
Simple cells in primary visual cortex were famously found to respond to low-level image components such as edges. Sparse coding and independent component analysis (ICA) emerged as the standard computational models for simple cell coding because they linked their receptive fields to the statistics of visual stimuli. However, a salient feature of image statistics, occlusions of image components, is not considered by these models. Here we ask if occlusions have an effect on the predicted shapes of simple cell receptive fields. We use a comparative approach to answer this question and investigate two models for simple cells: a standard linear model and an occlusive model. For both models we simultaneously estimate optimal receptive fields, sparsity and stimulus noise. The two models are identical except for their component superposition assumption. We find the image encoding and receptive fields predicted by the models to differ significantly. While both models predict many Gabor-like fields, the occlusive model predicts a much sparser encoding and high percentages of 'globular' receptive fields. This relatively new center-surround type of simple cell response is observed since reverse correlation is used in experimental studies. While high percentages of 'globular' fields can be obtained using specific choices of sparsity and overcompleteness in linear sparse coding, no or only low proportions are reported in the vast majority of studies on linear models (including all ICA models). Likewise, for the here investigated linear model and optimal sparsity, only low proportions of 'globular' fields are observed. In comparison, the occlusive model robustly infers high proportions and can match the experimentally observed high proportions of 'globular' fields well. Our computational study, therefore, suggests that 'globular' fields may be evidence for an optimal encoding of visual occlusions in primary visual cortex.

Show MeSH
Related in: MedlinePlus