Demo - Sample Stimuli from: Tanrikulu, Froyen, Feldman, & Singh " When is accreting/deleting texture seen as in front? Interpretation of depth from texture motion."

Experiment 1

One set of regions moving

  Number of Regions
Boundary
Shape
2 4 8
Straight
Curved-
Unbiased
Convex

 

Both sets of regions moving 

  Number of Regions
Boundary
Shape
2 4 8
Straight
Curved-
Unbiased
Convex

 

Experiment 2

One set of regions moving

  Number of Regions
Boundary
Shape
2 4 8
Straight
Curved-
Unbiased
Convex

 

Both sets of regions moving

  Number of Regions
Boundary
Shape
2 4 8
Straight
Curved-
Unbiased
Convex

Demo - Sample Stimuli from: Tanrikulu, Froyen, Feldman, & Singh "Geometric figure-ground cues override standard depth from accretion-deletion''

EXPERIMENT 1

(Click on any image to view the corresponding motion display.)

 Convex/symmetric regions contain motionNon-convex/asymmetric regions contain motionBoth sets of regions contain motion
Convexity & Symmetry
Symmetry

EXPERIMENT 2

(Click on any image to view the corresponding motion display.)

 Coherent MotionIncoherent Motion
Convexity & Symetry
Symetry

Demo - Information along contours

Information along contours

Attneave (1954) argued that information along contours is concentrated along points of locally maximal curvature. In a recent paper, we provide a formal proof of this, based on Shannon's definition of information (Feldman & Singh, Psychological Review, in press). This paper also extends Attneave's original claim by demonstrating the asymmetry in information content that arises from the sign of curvature. Whereas Attneave's analysis treated positive and negative curvature—i.e., convex and concave contour segments—symmetrically, we show that for closed contours, regions of negative curvature carry greater information than corresponding segments of positive curvature. MATLAB code for computing and plotting information along contours (i.e., the surprisal) is included below.

The option signed = 0 treats positive and negative curvature symmetrically (consistent with Attneave), whereas the option signed = 1takes into account (for closed contours) the sign of curvature as well, yielding a different distribution of information. The two figures below demonstrate this difference; the left one is produced from the unsigned version, the right one from the signed version.

curv shape info

The code assumes that the contour is sampled uniformly, in counter-clockwise direction, and is defined by a pair of vectors of equal length (x and y). resolution alters the number of neighboring points the code takes into account in computing the tangent direction at any given point.


function surprisal = contourinfoplot(x, y, signed, resolution)

x = x(:); y = y(:);

if length(x) ~= length(y)
error('the x and y vectors defining the contour must have equal lengths!');
end;

N = length(x);
b = 1; % spread term for the Von Mises distribution

if (x(1) == x(N) & y(1) == y(N))
N = N-1;
open = 0;
else
open = 1;
end

normalmap = [];
surprisalmap = [];

for j = 1:N

% define the previous and next points relative to the current one
xprev = 0;
yprev = 0;
xnext = 0;
ynext = 0;

for k = 1:resolution
prev(k) = j-k;
next(k) = j+k;
if(prev(k) < 1) prev(k) = prev(k) + N; end
if(next(k) > N) next(k) = next(k) - N; end

xprev = xprev + x(prev(k));
yprev = yprev + y(prev(k));
xnext = xnext + x(next(k));
ynext = ynext + y(next(k));
end

xprev = xprev/k;
yprev = yprev/k;
xnext = xnext/k;
ynext = ynext/k;


% vector _from_ the previous point; vector _to_ the next point
vecprev = [x(j), y(j)] - [xprev, yprev];
vecnext = [xnext, ynext] - [x(j), y(j)];

% compute the magnitude of the turning angle using dot product
alpha = acos( dot(vecprev, vecnext) / (norm(vecprev)*norm(vecnext)) ); 

% compute the sign of turning using cross product
% (assumes a counterclockwise sampling of the contour)
cp = cross( [vecprev, 0], [vecnext,0] );
alpha = sign(cp(3))*alpha;

% compute the surprisal using -log von mises
if(signed)
surprisal = -log( exp(b*cos(alpha - (2*pi/(N/resolution))) )/( 2*pi*besseli(0,b) ) );
else
surprisal = -log( exp(b*cos(alpha) )/( 2*pi*besseli(0,b) ) );
end;

% turning angles not defined near the end points of an open curve
if(open & (j - resolution < 1 | j + resolution > N)) surprisal = 0; end

% compute the tangent and normal vectors
tangvec = vecprev + vecnext;
tangvec = tangvec/norm(tangvec);
normvec = [[0 1; -1 0]*tangvec']';

normalmap = [normalmap; normvec];
surprisalmap = [surprisalmap; surprisal];

end;

% scale the size of histogram bars
surprisalmap = (1/range(surprisalmap))*(surprisalmap(:) - min(surprisalmap));
needlesize = max(range(x), range(y))/10;

% define the histogram normal to the shape
normalmap(:,1) = surprisalmap.*normalmap(:,1);
normalmap(:,2) = surprisalmap.*normalmap(:,2);
xnormals = [x(1:N), x(1:N) + needlesize*normalmap(:,1)];
ynormals = [y(1:N), y(1:N) + needlesize*normalmap(:,2)];

% plot
figure, plot(x,y,'r'), axis equal;
hold 
on, plot(xnormals', ynormals', 'k-');

Publications

bhg Bayesian Hierarchical Grouping: Perceptual grouping as mixture estimation
Froyen, V., Feldman, J., & Singh, M. (2015).
Psychological Review, 122(4), 575-597
PDF
itp Interface Theory of Perception
Hoffman, D., Singh, M., & Prakash, C. (in press)
Psychonomic Bulletin and Review
PDF
itp Probing the Interface Theory of Perception: Reply to Commentaries
Hoffman, D., Singh, M., & Prakash, C. (in press)
Psychonomic Bulletin and Review
PDF
shape transform Investigating shape representation using sensitivity to part- and axis-based transformations
Denisova, K., Feldman, J., Su, X, & Singh, M. (in press)
Vision Research
shape complexity The role of shape complexity in the detection of closed contours
Wilder, J., Feldman, J., & Singh, M. (in press)
Vision Research
stability com Perception of physical stability and center of mass of 3-D objects
Cholewiak, S., Fleming, R. & Singh, M. (2015)
Journal of Vision, 15(2):13, 1-11
JOV link
contour complexity Contour complexity and contour detection
Wilder, J., Feldman, J., & Singh, M. M. (2015)
Journal of Vision, 15(6):6, 1-16.
JOV link
Visual representation of contour and shape
Singh, M. (in press)
In: J. Wagemans (Ed.), Oxford Handbook of Perceptual Organization.
Oxford University Press.
Preprint
Perceptual grouping as Bayesian mixture estimation
Feldman, J., Singh, M., & Froyen, V. (in press)
In: S. Gepshtein, L. Maloney, & M. Singh (Eds.),
Oxford Handbook of Computational Perceptual Organization. Oxford University Press.
Preprint
Transparency and Translucency
Singh, M. (2014)
In: K. Ikeuchi (Ed.), Computer Vision: A Reference Guide, pp. 815-819. Springer Verlag.
Preprint
Rotating columns: Relating structure-from-motion, accretion/deletion, and figure/ground
Froyen, V., Feldman, J., & Singh, M. (2013)
Journal of Vision, 13(10):6 1-12.
JOV link
Visual perception of the physical stability of asymmetric three-dimensional objects
Cholewiak, S., Fleming, R., & Singh, M. (2013)
Journal of Vision, 13(4):12, 1-13.
JOV link
Perceived causality can alter the perceived trajectory of apparent motion
Kim, S.-H., Feldman, J., & Singh, M. (2013)
Psychological Science, 24(4), 575-582.
PDF
Natural selection and shape perception
Singh, M. & Hoffman, D. (2013)
In: Shape Perception in Human and Computer Vision: An Interdisciplinary Perspective. S. Dickinson & Z. Pizlo (Eds.). Springer Verlag.
Preprint Book
An integrated Bayesian approach to shape representation and perceptual organization
Feldman, J., Singh, M., Briscoe, E., Froyen, V., Kim, S. & Wilder, J. (2013)
In: Shape Perception in Human and Computer Vision: An Interdisciplinary Perspective. S. Dickinson & Z. Pizlo (Eds.). Springer Verlag. Preprint Book
A century of Gestalt psychology in visual perception: I. Perceptual grouping and figure-ground organization
Wagemans, J., Elder, J., Kubovy, M., Palmer, S., Peterson, M., Singh, M., & von der Heydt, R. (2012)
Psychological Bulletin, 138(6), 1172-1217. PDF
Computational evolutionary perception
Hoffman, D. & Singh, M. (2012)
Perception, 41(9), 1073-1091.
(Special Issue on the 30th anniversary of Marr's "Vision")
PDF
Principles of Contour Information: A response to Lim & Leek (2012)
Singh, M. & Feldman, J. (2012)
Psychological Review, 119(3), 678-683.
PDF
Curved apparent motion induced by amodal completion
Kim, S.-H., Feldman, J., & Singh, M. (2012)
Attention, Perception, & Psychophysics, 74(2), 350-364.
PDF
Perceptual models of viewpoint preference
Secord, A., Lu, C., Finkelstein, A., Singh, M. & Nealen, A. (2011)
ACM Transcations on Graphics, 30(5), 109:1-12.
PDF
Superordinate shape classificiation using natural shape statistics
Wilder, J., Feldman, J., & Singh, M. (2011)
Cognition, 119(3), 325-340.
PDF
Perceived object stability depends on multisensory estimates of gravity
Barnett-Cowan, M., Fleming, R. W., Singh, M., & Buelthoff, H. H. (2011)
PLoS ONE, 6(4), e19289, 1-5.
PLoS ONE link
Robust visual estimation as source separation
Juni, M. Z., Singh, M., & Maloney, L. T. (2010)
Journal of Vision, 10(14):2, 1-20.
JOV link
A Bayesian framework for figure-ground interpretation
Froyen, V., Feldman, J., & Singh, M. (2010)
Advances in Neural Information Processing Systems, 23.
PDF
How well do line drawings depict shape?
Cole, F., Sanik, K., DeCarlo, D., Finkelstein, A., Funkhouser, T., Rusinkiewicz, S., & Singh, M. (2009)
ACM Transactions on Graphics, 28(3) (proc. SIGGRAPH).
PDF
An experimental criterion for consistency in interpolation of partially-occluded contours
Fulvio, J., Singh, M., & Maloney, L. T. (2009)
Journal of Vision, 9(4):5, 1-19.
JOV link
Perceptual segmentation and the perceived orientation of dot clusters: The role of robust statistics
Cohen, E., Singh, M., & Maloney, L. T. (2008)
Journal of Vision, 8(7):6, 1-13. (Special Issue: Perceptual Organization and Neural Computation)
JOV link
Precision and consistency of contour interpolation
Fulvio, J., Singh, M., & Maloney, L. T. (2008)
Vision Research, 48, 831-849.
PDF
Natural decompositions of perceived transparency: Reply to Albert (2008)
Anderson, B. L., Singh, M., & O'Vari, J. (2008)
Psychological Review, 115, 1144-1153.
PDF
Geometric determinants of shape segmentation: Tests using segment identification
Cohen, E. and Singh, M. (2007)
Vision Research, 47, 2825-2840.
Abstract | PDF
The relationship between spatial pooling and attention in saccadic and perceptual tasks
Cohen, E., Schnitzer, B., Gersch, T., Singh, M. and Kowler, E. (2007)
Vision Research, 47, 1907-1923.
Abstract | PDF
Bayesian contour extrapolation: Geometric determinants of good continuation
Singh, M. and Fulvio, J. (2007)
Vision Research, 47, 783-798.
Abstract | PDF
Bayesian estimation of the shape skeleton
Feldman, J. and Singh, M. (2006)
Proceedings of the National Academy of Sciences, 103, 18014-18019.
Abstract | PDF
Perceived orientation of complex shape reflects graded part decomposition
Cohen, E. H. and Singh, M. (2006)
Journal of Vision, 6, 805-821.
JOV link
The role of part structure in the perceptual localization of a shape
Denisova, K., Singh, M., & Kowler, E. (2006)
Perception, 35, 1073-1087.
Abstract | Perception link
Contour extrapolation using probabilistic cue combination
Singh, M. and Fulvio, J. M. (2006)
Computer Vision and Pattern Recognition, Proceedings.
Abstract | PDF | DOI link
Consistency of location and gradient judgments of visually-interpolated contours
Fulvio, J. M., Singh, M., & Maloney, L. T. (2006)
Computer Vision and Pattern Recognition, Proceedings.
Abstract | PDF | DOI link
Surface geometry influences the shape of illusory contours
Fulvio, J. M. and Singh, M. (2006)
Acta Psychologica, 123, 20-40.
(Special Issue: Michotte's heritage in perception and cognition research)
Abstract | PDF
Combining achromatic and chromatic cues to transparency
Fulvio, J. M., Singh, M., & Maloney, L. T. (2006)
Journal of Vision, 6, 760-776.
JOV link

Photometric determinants of perceived transparency
Singh, M., and Anderson, B. L. (2006)
Vision Research, 46, 879-894.
Abstract | PDF

The perceived transmittance of inhomogeneous surfaces and media
Anderson, B. L., Singh, M., & Meng, J. (2006)
Vision Research, 46, 1982-1995.
Abstract |  PDF
Visual extrapolation of contour geometry
Singh, M., and Fulvio, J. M. (2005)
Proceedings of the National Academy of Sciences, 102, 939-944.
Abstract |  PDF (Supporting Information: pdf / PNAS website)
Information along contours and object boundaries
Feldman, J., and Singh, M. (2005)
Psychological Review, 112, 243-252.
Abstract | PDF
  What change detection tells us about the visual representation of shape
Cohen, E. H., Barenholtz, E., Singh, M., & Feldman, J. (2005)
Journal of Vision, 5, 313-321.
JOV link
 

Lightness constancy through transparency: Internal consistency in layered surface representations
Singh, M. (2004)
Vision Research, 44, 1827-1842.
Abstract | PDF

  Modal and amodal completion generate different shapes
Singh, M. (2004)
Psychological Science, 15, 454-459.
Abstract | PDF
  Computing layered surface representations: An algorithm for detecting and separating transparent overlays
Singh, M., and Huang, X. (2003)
Computer Vision and Pattern Recognition, Proceedings '03, Vol II, 11-18.
Abstract | PDF
  Detection of change in shape: An advantage for concavities
Barenholtz, E., Cohen, E., Feldman, J., & Singh, M. (2003)
Cognition, 89, 1-9.
Abstract |  PDF
  Vision: Form perception
Hoffman, D., and Singh, M. (2002)
In: Encyclopedia of Cognitive Science, Volume 4, L. Nadel (Ed.), 486-490. London: Macmillan Publishers Limited.
  Early computation of part structure: Evidence from visual search
Xu, Y., and Singh, M. (2002)
Perception and Psychophysics, 64, 1039-1054.
Abstract |  PDF
  Toward a perceptual theory of transparency
Singh, M., and Anderson, B. (2002)
Psychological Review, 109, 492-519.
Abstract |  PDF
  The interpolation of object and surface structure
Anderson, B., Singh, M., & Fleming, R. (2002)
Cognitive Psychology, 44, 148-190.
Abstract |  PDF
  Perceptual assignment of opacity to translucent surfaces: The role of image blur
Singh, M., and Anderson, B. (2002)
Perception, 31, 531-552.
Abstract | PDF
  Part-based representations of visual shape and implications for visual cognition
Singh, M., and Hoffman, D. (2001)
In: From fragments to objects: Grouping and segmentation in vision. Advances in Psychology Series,Volume 130. T. Shipley & P. Kellman (Eds.), 401-459. New York: Elsevier Science.
Abstract | PDF
  Constructing surfaces and contours in displays of color from motion: The role of nearest neighbors
Fidopiastis, C., Hoffman, D., Prophet, W., & Singh, M. (2000)
Perception, 29, 567-580.
Abstract | PDF
  Completing visual contours: The relationship between relatability and minimizing inflections
Singh, M., & Hoffman, D. (1999)
Perception and Psychophysics, 61, 943-951.
Abstract | PDF
  Parsing silhouettes: The short-cut rule
Singh, M., Seyranian, G., & Hoffman, D. (1999)
Perception and Psychophysics, 61, 636-660.
Abstract |  PDF
  Contour completion and relative depth: Petter's rule and support ratio
Singh, M., Hoffman, D., & Albert, M. (1999)
Psychological Science, 10, 423-428.
  Part boundaries alter the perception of transparency
Singh, M., & Hoffman, D. (1998)
Psychological Science, 9, 370-378.
  Abstract  |  PDF
  Constructing and representing visual objects
Singh, M., & Hoffman, D. (1997)
Trends in Cognitive Sciences, 1, 98-102.
  Salience of visual parts
Hoffman, D., & Singh, M. (1997)
Cognition, 63, 29-78.
Abstract | PDF

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