Are V1 Simple Cells Optimized for Visual Occlusions? A Comparative Study
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{"title"=>"Are V1 Simple Cells Optimized for Visual Occlusions? A Comparative Study", "type"=>"journal", "authors"=>[{"first_name"=>"Jörg", "last_name"=>"Bornschein", "scopus_author_id"=>"56989350700"}, {"first_name"=>"Marc", "last_name"=>"Henniges", "scopus_author_id"=>"36655745000"}, {"first_name"=>"Jörg", "last_name"=>"Lücke", "scopus_author_id"=>"13104958300"}], "year"=>2013, "source"=>"PLoS Computational Biology", "identifiers"=>{"sgr"=>"84879535272", "pui"=>"369208155", "scopus"=>"2-s2.0-84879535272", "issn"=>"1553734X", "doi"=>"10.1371/journal.pcbi.1003062", "pmid"=>"23754938"}, "id"=>"b4cd65bd-c860-33d0-8da4-78d9a9ac15a4", "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.", "link"=>"http://www.mendeley.com/research/v1-simple-cells-optimized-visual-occlusions-comparative-study", "reader_count"=>32, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>3, "Researcher"=>10, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>8, "Student > Master"=>2, "Other"=>2, "Student > Bachelor"=>4, "Professor"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>3, "Researcher"=>10, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>8, "Student > Master"=>2, "Other"=>2, "Student > Bachelor"=>4, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>6, "Mathematics"=>1, "Agricultural and Biological Sciences"=>6, "Medicine and Dentistry"=>3, "Neuroscience"=>2, "Physics and Astronomy"=>4, "Psychology"=>3, "Computer Science"=>7}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>6}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Neuroscience"=>{"Neuroscience"=>2}, "Physics and Astronomy"=>{"Physics and Astronomy"=>4}, "Psychology"=>{"Psychology"=>3}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>6}, "Computer Science"=>{"Computer Science"=>7}, "Mathematics"=>{"Mathematics"=>1}}, "reader_count_by_country"=>{"Canada"=>1, "United States"=>3, "France"=>1, "Belarus"=>1, "Germany"=>2}, "group_count"=>6}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1075960"], "description"=>"<p><b>A</b> Image patch (bottom left) showing an intersection of two branches extracted from a grey-level natural scene image (adapted from the van Hateren natural image database <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062-vanHateren1\" target=\"_blank\">[58]</a> with permission from J. H. van Hateren). Preprocessed version of the image patch (bottom right) obtained by using a center-surround filter to model the preprocessing by the lateral geniculate nucleus. <b>B</b> Left: Two image patches manually generated from the grey-level patch in <b>A</b>. Each patch is dominated by one of the two crossing branches of the original patch. Middle: The preprocessed versions of the two patches (central parts). Right: Combination of the two preprocessed patches using an occlusive combination (top) and a standard linear combination (bottom). <b>C</b> Examples of globular and Gabor-like receptive fields measured in V1 of macaque monkeys (courtesy of D. Ringach), and examples of the two receptive field types predicted by the occlusive encoding model. <b>D</b> Percentages of globular receptive fields predicted by different models for hidden units compared to percentages of globular fields of <i>in vivo</i> recordings.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "computational", "receptive"], "article_id"=>712905, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_the_combination_of_image_components_comparison_with_computational_models_of_component_combinations_and_receptive_field_comparison_/712905", "title"=>"Illustration of the combination of image components, comparison with computational models of component combinations, and receptive field comparison.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-06-06 00:48:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/1075961"], "description"=>"<p>Suppose all hidden units are zero except of units and . In this case the patch is generated using the basis functions and . If the two basis functions have the form as displayed on the right-hand-side, the non-linear and the linear model generate the patches on the left-hand-side. Given a pixel , the non-linear model chooses the basis function with the maximal absolute value () to set the value of the patch, . For the example pixel (red box), is chosen but for other pixels may be chosen. Note that the -superposition models the exclusiveness of occlusion without considering object or edge depths. The linear model always sums the basis function values, . After the generation of the noiseless patches both models assume the addition of Gaussian noise for the generation of patches (see <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062.e006\" target=\"_blank\">Eqns. 2</a> and <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062.e008\" target=\"_blank\">4</a> but not shown in the figure). The color scale is defined as in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi-1003062-g001\" target=\"_blank\">Fig. 1</a>.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "non-linear", "linear", "generative"], "article_id"=>712906, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Example_of_the_non_linear_and_the_linear_generative_model_/712906", "title"=>"Example of the non-linear and the linear generative model.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-06-06 00:48:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/1075962"], "description"=>"<p><b>A</b> Receptive fields predicted if occlusion-like superposition is assumed ( out of receptive fields are shown). <b>B</b> Receptive fields predicted if standard linear superposition is assumed ( out of receptive fields are shown). <b>C</b> Percentages of globular fields predicted by the occlusive model (MCA) and by the linear model (BSC) versus number of hidden units. The experiments for MCA (blue line) and BSC (green line) on DoG preprocessed image patches were repeated five times and the error bars extend two empirical standard deviations. Standard sparse coding (yellow line) on DoG processed data shows the lowest fraction of globular fields. To control for the influence of preprocssing, additional experiments were performed on ZCA whitened data (dashed blue and dashed green lines). The bold red line (and its error bar) shows the fraction of globular fields computed based on <i>in vivo</i> measurements of macaque monkeys <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062-Ringach1\" target=\"_blank\">[14]</a>. Dashed red lines show the fractions reported for ferrets <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062-Usrey1\" target=\"_blank\">[15]</a> and mice <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062-Niell1\" target=\"_blank\">[16]</a>.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "globular", "receptive", "fields", "computational"], "article_id"=>712907, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Percentages_of_globular_receptive_fields_predicted_by_the_computational_models_in_comparison_to_in_vivo_measurements_/712907", "title"=>"Percentages of globular receptive fields predicted by the computational models in comparison to <i>in vivo</i> measurements.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-06-06 00:48:27"}
  • {"files"=>["https://ndownloader.figshare.com/files/1075963"], "description"=>"<p><b>A</b> Analysis of learned Gabor-like receptive fields for experiments with hidden units (and patch size ): distribution of Gabor shaped receptive fields learned by occlusion-like (MCA) and linear sparse coding (BSC). The red triangles in both plots depict the distribution computed based on <i>in vivo</i> measurements of macaque monkeys <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003062#pcbi.1003062-Ringach1\" target=\"_blank\">[14]</a>. <b>B</b> Average number of active units accross image patches as a function of the number of hidden units (note that error bars are very small; experiments on pixel sized DoG preporcessed patches).</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "gabor", "recordings"], "article_id"=>712908, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_Gabor_shape_statistics_with_in_vivo_recordings_and_predicted_sparsity_/712908", "title"=>"Comparison of Gabor shape statistics with <i>in vivo</i> recordings and predicted sparsity.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-06-06 00:48:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/1075964"], "description"=>"<p>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.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "patches", "components"], "article_id"=>712909, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Decomposition_of_image_patches_into_basic_components_for_four_example_patches_/712909", "title"=>"Decomposition of image patches into basic components for four example patches.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-06-06 00:48:29"}
  • {"files"=>["https://ndownloader.figshare.com/files/1075965"], "description"=>"<p><b>A</b> Selection of typical preprocessed image patches. <b>B</b> Superposition of two Gabor fields as assumed by standard sparse coding with continuous priors (along with additive Gaussian noise after superposition). <b>C</b> Superposition of the same two Gabor fields if hidden units (prefactors) are binary. <b>D</b> Superposition of the Gabor fields if a point-wise maximum is used as superposition model.</p>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "superposition", "globular"], "article_id"=>712910, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_different_superposition_models_and_globular_fields_/712910", "title"=>"Illustration of different superposition models and globular fields.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-06-06 00:48:30"}
  • {"files"=>["https://ndownloader.figshare.com/files/1075966", "https://ndownloader.figshare.com/files/1075967", "https://ndownloader.figshare.com/files/1075968", "https://ndownloader.figshare.com/files/1075969", "https://ndownloader.figshare.com/files/1075970", "https://ndownloader.figshare.com/files/1075971", "https://ndownloader.figshare.com/files/1075972"], "description"=>"<div><p>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.</p></div>", "links"=>[], "tags"=>["Computational biology", "computational neuroscience", "Coding mechanisms", "Sensory systems", "neuroscience", "Visual system", "Probability theory", "statistics", "Statistical methods", "v1", "cells", "optimized", "comparative"], "article_id"=>712911, "categories"=>["Mathematics", "Biological Sciences"], "users"=>["Jörg Bornschein", "Marc Henniges", "Jörg Lücke"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1003062.s001", "https://dx.doi.org/10.1371/journal.pcbi.1003062.s002", "https://dx.doi.org/10.1371/journal.pcbi.1003062.s003", "https://dx.doi.org/10.1371/journal.pcbi.1003062.s004", "https://dx.doi.org/10.1371/journal.pcbi.1003062.s005", "https://dx.doi.org/10.1371/journal.pcbi.1003062.s006", "https://dx.doi.org/10.1371/journal.pcbi.1003062.s007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Are_V1_Simple_Cells_Optimized_for_Visual_Occlusions_A_Comparative_Study_/712911", "title"=>"Are V1 Simple Cells Optimized for Visual Occlusions? A Comparative Study", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-06-06 00:48:31"}

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Relative Metric

{"start_date"=>"2013-01-01T00:00:00Z", "end_date"=>"2013-12-31T00:00:00Z", "subject_areas"=>[{"subject_area"=>"/Biology and life sciences", "average_usage"=>[269, 466, 588, 697, 800, 896, 988, 1076, 1165, 1254, 1340, 1417]}, {"subject_area"=>"/Biology and life sciences/Computational biology", "average_usage"=>[295, 511, 651, 775, 882, 992, 1100, 1201, 1304, 1400, 1486, 1570, 1650]}, {"subject_area"=>"/Biology and life sciences/Neuroscience", "average_usage"=>[261, 444, 554, 655, 748, 834, 923, 1004, 1089, 1170, 1244, 1315, 1380]}, {"subject_area"=>"/Engineering and technology", "average_usage"=>[254, 440, 558, 675, 785, 883, 972, 1061, 1154, 1248, 1336, 1414, 1489]}, {"subject_area"=>"/Engineering and technology/Software engineering", "average_usage"=>[289, 479, 594, 761, 915, 998, 1133, 1262, 1368, 1465, 1562, 1644, 1724]}, {"subject_area"=>"/Medicine and health sciences", "average_usage"=>[264, 460, 584, 692, 794, 887, 978, 1067, 1154, 1241, 1328, 1408, 1474]}]}

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