Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group
Journal Home About Issues in Progress Current Issue All Issues Feature Issues

A geometric framework for nonlinear visual coding

Erhardt Barth and Andrew B. Watson

Open Access Open Access

Abstract

It is argued that important aspects of early and middle level visual coding may be understood as resulting from basic geometric processing of the visual input. The input is treated as a hypersurface defined by image intensity as a function of two spatial coordinates and time. Analytical results show how the Riemann curvature tensor R of this hypersurface represents speed and direction of motion. Moreover, the results can predict the selectivity of MT neurons for multiple motions and for motion in a direction along the optimal spatial orientation. Finally, a model based on integrated R components predicts global-motion percepts related to the barber-pole illusion.

©2000 Optical Society of America

Full Article  |  PDF Article
More Like This
Riemann tensor of motion vision revisited

Michael H. Brill
Opt. Express 9(1) 7-8 (2001)

Visual communication with retinex coding

Friedrich O. Huck, Carl L. Fales, Richard E. Davis, and Rachel Alter-Gartenberg
Appl. Opt. 39(11) 1711-1730 (2000)

Anisotropies in visual motion perception: a fresh look

Bryan L. Gros, Randolph Blake, and Eric Hiris
J. Opt. Soc. Am. A 15(8) 2003-2011 (1998)

View More...

Supplementary Material (4)

Media 1: MOV (179 KB)     
Media 2: MOV (168 KB)     
Media 3: MOV (147 KB)     
Media 4: MOV (144 KB)     

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)
Fig. 1.
Fig. 1. (180 K) The movie shows the six Riemann-tensor components for a square (shown on the left) that appears and moves in different directions. The arrangement of the components is as in Eq. (2).

Download Full Size | PDF

Fig. 2.
Fig. 2. (196 K) The movie shows a moving square with colored circles (red, green, blue for intrinsic dimensions 3, 2, 1) indicating the intrinsic dimension of different movie regions.

Download Full Size | PDF

Fig. 3.
Fig. 3. (2*148 K) Two movies showing the Barber-pole illusion (left) and the Kooi effect (right). While in both cases the grating moves horizontally to the left behind the gray aperture, we see it moving down left in the direction of the oblique aperture in left movie. If the shape of the aperture is changed as in the right movie, the grating is seen to move horizontally. [Media 3] [Media 4]

Download Full Size | PDF

Fig. 4.
Fig. 4. Simulation results for the two movies in Fig. 3. Note that small changes in the shape of the aperture change the resulting global direction of motion.

Download Full Size | PDF

Fig. 5.
Fig. 5. Data by Albright [38] are shown in the right columns for direction (top) and orientation (bottom) selectivity of macaque MT neurons (that are selective to motion along the preferred spatial orientation) and simulation results in the left columns - see text.

Download Full Size | PDF

Fig. 6.
Fig. 6. Data by Recanzone et al. illustrating the selectivity of MT neurons to multiple motions are shown on the right and simulation results obtained as in Fig. 5 (but for a rotation by 135 degree) on the left. As indicated by the arrows on the left, blue is chosen for the case of a single moving dot, red for the case with an additional dot moving opposite to the preferred direction, and green for the case with an additional dot moving along the preferred direction.

Download Full Size | PDF

Tables (1)

Tables Icon

Table 1. Summary of correspondences between motions and curvatures.

View Table

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

( x , y , t , f ( x , y , t ) )
R 2121 = f xx f yy − f xy 2 1 + f x 2 + f y 2 + f 1 2 ; R 3131 = f xx f tt − f xt 2 1 + f x 2 + f y 2 + f t 2 ; R 3232 = f yy f tt − f yt 2 1 + f x 2 + f y 2 + f t 2 ;
R 3231 = f xy f tt − f xt f yt 1 + f x 2 + f y 2 + f 1 2 ; R 3121 = f xx f yt − f xt f xy 1 + f x 2 + f y 2 + f t 2 ; R 3221 = f xy f yt − f yy f xt 1 + f x 2 + f y 2 + f t 2 .
f : f ( x − tv cos θ , y − tv sin θ )
R 3221 R 2121 = R 3232 R 3221 = R 3231 R 3121 = ν cos ( θ ) ; R 3232 R 2121 = ν 2 cos ( θ ) 2 ;
R 3121 R 2121 = R 3131 R 3121 = R 3231 R 3221 = − ν sin ( θ ) ; R 3131 R 2121 = ν 2 sin ( θ ) 2 .
R 3131 R 3231 = − R 3121 R 3221 = − R 3231 R 3232 = tan ( θ ) ; R 3131 R 3232 = tan ( θ ) 2 .
R 3131 + R 3232 = v 2 R 2121 .
Select as filters
Select Topics Cancel
Top
       
© Copyright 2024 | Optica Publishing Group. All rights reserved, including rights for text and data mining and training of artificial technologies or similar technologies.
Privacy | Terms of Use