The Role of the Harmonic Vector Average in Motion Integration
The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2013-10-01
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| Series: | Frontiers in Computational Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fncom.2013.00146/full |
| _version_ | 1819266014791073792 |
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| author | Alan eJohnston Peter eScarfe |
| author_facet | Alan eJohnston Peter eScarfe |
| author_sort | Alan eJohnston |
| collection | DOAJ |
| description | The local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The harmonic vector average however provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the intersection of constraints direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the harmonic vector average. |
| first_indexed | 2024-12-23T20:54:32Z |
| format | Article |
| id | doaj.art-041231616cf148e5846110826c8160bd |
| institution | Directory Open Access Journal |
| issn | 1662-5188 |
| language | English |
| last_indexed | 2024-12-23T20:54:32Z |
| publishDate | 2013-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computational Neuroscience |
| spelling | doaj.art-041231616cf148e5846110826c8160bd2022-12-21T17:31:33ZengFrontiers Media S.A.Frontiers in Computational Neuroscience1662-51882013-10-01710.3389/fncom.2013.0014650734The Role of the Harmonic Vector Average in Motion IntegrationAlan eJohnston0Peter eScarfe1University College LondonUniversity of ReadingThe local speeds of object contours vary systematically with the cosine of the angle between the normal component of the local velocity and the global object motion direction. An array of Gabor elements whose speed changes with local spatial orientation in accordance with this pattern can appear to move as a single surface. The apparent direction of motion of plaids and Gabor arrays has variously been proposed to result from feature tracking, vector addition and vector averaging in addition to the geometrically correct global velocity as indicated by the intersection of constraints (IOC) solution. Here a new combination rule, the harmonic vector average (HVA), is introduced, as well as a new algorithm for computing the IOC solution. The vector sum can be discounted as an integration strategy as it increases with the number of elements. The vector average over local vectors that vary in direction always provides an underestimate of the true global speed. The harmonic vector average however provides the correct global speed and direction for an unbiased sample of local velocities with respect to the global motion direction, as is the case for a simple closed contour. The HVA over biased samples provides an aggregate velocity estimate that can still be combined through an IOC computation to give an accurate estimate of the global velocity, which is not true of the vector average. Psychophysical results for type II Gabor arrays show perceived direction and speed falls close to the intersection of constraints direction for Gabor arrays having a wide range of orientations but the IOC prediction fails as the mean orientation shifts away from the global motion direction and the orientation range narrows. In this case perceived velocity generally defaults to the harmonic vector average.http://journal.frontiersin.org/Journal/10.3389/fncom.2013.00146/fullplaidsglobal motionmotion integrationintersection of contraintsaperture problem |
| spellingShingle | Alan eJohnston Peter eScarfe The Role of the Harmonic Vector Average in Motion Integration Frontiers in Computational Neuroscience plaids global motion motion integration intersection of contraints aperture problem |
| title | The Role of the Harmonic Vector Average in Motion Integration |
| title_full | The Role of the Harmonic Vector Average in Motion Integration |
| title_fullStr | The Role of the Harmonic Vector Average in Motion Integration |
| title_full_unstemmed | The Role of the Harmonic Vector Average in Motion Integration |
| title_short | The Role of the Harmonic Vector Average in Motion Integration |
| title_sort | role of the harmonic vector average in motion integration |
| topic | plaids global motion motion integration intersection of contraints aperture problem |
| url | http://journal.frontiersin.org/Journal/10.3389/fncom.2013.00146/full |
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