We are developing a frontend that is based on the image representation in the
visual cortex and plausible processing schemes. This frontend consists of multiscale
line/edge and keypoint (vertex) detection, using models of simple, complex
and end-stopped cells. This frontend is being extended by a new disparity model.
Assuming that there is no neural inverse tangent operator, we do not exploit Gabor
phase information. Instead, we directly use simple cell (Gabor) responses at
positions where lines and edges are detected

du Buf, J. M. H.

Rodrigues, J. M. F.

Universidade do Algarve

A VISION FRONTEND WITH A NEW DISPARITY
MODEL
Joa˜o Rodrigues and J.M. Hans du Buf
University of Algarve, Faro, Portugal
jrodrig@ualg.pt dubuf@ualg.pt
Abstract
We are developing a frontend that is based on the image representation in the
visual cortex and plausible processing schemes. This frontend consists of multi-
scale line/edge and keypoint (vertex) detection, using models of simple, complex
and end-stopped cells. This frontend is being extended by a new disparity model.
Assuming that there is no neural inverse tangent operator, we do not exploit Ga-
bor phase information. Instead, we directly use simple cell (Gabor) responses at
positions where lines and edges are detected.
1 Introduction
During the last decade, the modeling of processes in the visual cortex has become
a mature research topic. Mostly on the basis of Gabor quadrature filters as a model
of simple cells, models of complex cells and end-stopped cells have been developed,
e.g. (Heitger et al., 1992). In addition, models for line/edge detection (Deemter and
du Buf, 1996) and bar and grating cells (Petkov and Kruizinga, 1997) have become
available. Hence, it is now possible to develop a vision frontend that integrates all types
of processing and that can be used to explore higher-level tasks like object recognition.
Because of the ocular dominance columns in the primary cortex (Hubel, 1995),
which bring retinotopic, orientation-specific projections of the left and right eye closely
together such that neural dendritic fields can cover both, we can assume that disparity
estimation is already done in, or starts at, the first layers. However, we do not yet
know how this is done (Qian, 1997). One approach in computer vision is based on
the derivative of the local Gabor phase, also called the instantaneous frequency (Fleet
et al., 1991). This method needs a coarse-to-fine scale stabilization and has problems
in regions where the Gabor amplitude is very small, but it can provide a very rich
and continuous disparity estimate. The Ohzawa-type model (Ohzawa et al., 1997)
also employs quadrature Gabor filters, but it is more straightforward because disparity-
sensitive complex cells are modeled by summing the squared responses of disparity-
sensitive simple cells, the latter combining (positive) on and off Gabor responses of
the left and right images. However, this model is still rather “academic” because it has
not been tested with real images (the most complex example tested was a random dot
stereogram, showing a very unstable disparity at the border, see (Qian, 1997)). It is
likely that the Ohzawa-type model also needs a lot of postprocessing before it can be
applied to real images.
Instead of experimenting with the Ohzawa-type model and the necessary stabiliza-
tion, we decided to explore an alternative that is not based on phase nor amplitude
summations. The basic idea is extremely simple: once we have line/edge detection, we
have also access to the central, linear part of the Gabor responses, i.e. the sinusoidal or
imaginary response in the case of lines and the sinusoidal-like or real response in the
1
case of an edge. Below we first introduce the basic keypoint and line/edge extraction
with the necessary stabilizations, and then the new disparity model.
2 Lines, edges and keypoints
Line, edge and keypoint detection are based on the responses of simple, complex and
end-stopped cells. Gabor filters provide a simple model of cortical simple cells. In the
spatial domain they consist of a real cosine and an imaginary sine, both with a Gaussian
envelope. Since all filtering is done in the frequency domain, we apply polar-separable
transfer functions
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the number of scales and orientations. We apply a
linear scaling between
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, with the possibility of using many contiguous
scales or a few noncontiguous scales with neighboring micro-scales, see below. We
use
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.
In the spatial domain, the responses of even and odd simple cells, which correspond
to the real and imaginary parts of the Gabor filters, are denoted by IKJ<  
MLN
OP
and
IRQ
<
 
LN
6OP
TS
being the scale and 0 the orientation (i.e. U RV   and U   0,W "	587X
9 ). In order to simplify the notation, and because the same processing is done at all
scales, we drop the subscript
S
. The responses of complex cells are modelled by the
modulus Y

MLN
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I
J

MLN
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. There are two types of end-
stopped cells (Heitger et al., 1992; Wu¨rtz and Lourens, 1997) , i.e. single (S) and
double (D). Introducing f #Hghi U  and j #kilnm U  , these cells are modelled by
op6LN
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in which
[
c
y denotes the suppression of negative values. The distance t is scaled
linearly with the filter scale
S
, i.e. t

1
2 S
. All end-stopped responses along straight
lines and edges need to be suppressed, for which we use tangential (T) and radial (R)
inhibition:
LN
6OPq
 ~4pŁ

np
[
Y

@Bb
~
LN
O
a
Y

@Bb
v
ML
awt
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6O
aut
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
LN
6OPq
 svpŁ

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|
Y

@Bb
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
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6OP~
Y

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where

0
a
5
7
"&$Nh5
7
V
0
h5
7
. Instead of applying the inhibition to individ-
ual end-stopped cells (Heitger et al., 1992; Wu¨rtz and Lourens, 1997), slightly better
results are obtained by applying




a


once to the pooled activity:

LN
O>
~Ł

p
opsML#
6OP~+

ML#
6OP
and
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z
6LN
6OP~+

LN
6OP

2
with ¡+¢¤£¦¥ § , after which the keypoint map is obtained: ¨?©MªN«¬P­¯®±°³²&´Tµ¶¨ﬃ·N©MªN«¬P­b«
¨ ¸R©ªN«6¬P­b¹« i.e. at each filter scale º : ¨¼»¶©MªN«¬P­ .
Postprocessing of ¨?©Mª#«6¬P­ is necessary because our goal is to obtain a clean, single-
pixel keypoint map with no spurious points. In addition, for pattern recognition appli-
cations we want to classify the keypoints according to the underlying vertex structure,
i.e. K, L, T, + etc. Postprocessing is done in six steps, at each scale, after which dif-
ferent scales are combined by considering, around each scale, a small scale interval: 4
micro-scales, i.e. two scales slightly finer and two slightly coarser than the actual scale.
In the case of the smallest (largest) scale four coarser (finer) scales are applied. Only
keypoints which are consistent over 3 neighboring micro-scales are accepted.
Line and edge detection is based on simple cells (Deemter and du Buf, 1996).
A positive line is detected where ½*¾ shows a local maximum and ½*¿ shows a zero
crossing. In the case of an edge the even and odd responses must be swapped. This
gives 4 possibilities for positive and negative events: local maxima/minima plus zero
crossings. We also combine the responses of simple and complex cells, i.e. the simple
cells serve to detect positions and event types, whereas the complex cells are used to
increase the confidence. Since the use of Gabor modulus (complex cells) implies a loss
of precision at vertices (du Buf, 1993) we increase precision by considering multiple
scales. Our improved detection scheme consists of 5 processing steps for each scale,
after which the coherence is improved by checking 4 neighboring micro-scales.
3 Disparity estimation
Our disparity model is based on the central, linear part of the Gabor responses, i.e.
the sinusoidal part with ÀÁnÂÃªw¢±ª#«Ä ªvÄvÅÇÆ#È¶§ . Assuming ideal events, i.e. lines with
a Dirac profile and edges with a Heaviside step profile, or nonideal ones obtained by
Gaussian filtering, and complex Gabor filters with the same orientation, the responses
are (scaled) Gabor functions and complex errorfunctions. The latter can be approxi-
mated by scaled Gabor functions (du Buf, 1993). In other words, both line and edge
responses are essentially scaled Gabor functions. One step in line/edge detection con-
sists of checking the Gabor response ½*¿É ©Mª#«6¬P­ (the odd, imaginary part in the case of
a line), or ½R¾É ©Mª#«6¬P­ (the even, real (!) part in the case of an edge) for a zero crossing
on ÊRËÌÈ¶§ . Here, for disparity, we apply the same event detection steps to two images,
left and right. In the case of the left image, we (1) check the existence of an event of
the same type in the right image on ÊRËÈ&Í , and (2) if so, we take the value of Ê¯½ ¿ or
Ê¯½R¾ of the right image at the event (zero crossing) position in the left image. The sign
depends on the event polarity and, in order to obtain values which do not depend on
the event amplitude, Ê¯½R¿ or Ê¯½R¾ is divided by the modulus (complex cell response)
of the left image, which is maximum at the event position. After this normalization yet
another one is applied: the response is divided by the scale º of the filter. Hence, the
slope of the linear response part will not depend on the event amplitude nor on the filter
scale, i.e. disparity estimates obtained at different scales will be the same. The same
processing can be done in the case of the right image, by exchanging left and right. Of
course, the disparity estimates need to be calibrated once using real data, like the way
babies need to learn in the first months.
3
Figure 1: Top: sign2 image and line/edge detection. Bottom: keypoints detected with
event directions, after multi-scale stabilization (zoomed).
One problem we encountered were small fluctuations of the disparity estimates,
especially at the finest scales. These are due to the fact that we need to work at discrete
pixel positions, and the maximum of the modulus used in the first normalization is
therefore not the theoretical maximum. We solved this by averaging disparity estimates
over neighboring scales.
4 Results and discussion
Figure 1 shows results of line/edge and keypoint detection. Single- and multi-scale
stabilization has eliminated many spurious keypoints, one of which is shown by the
small diamond of 4 pixels (bottom image). All keypoints of the van have been detected,
4
Figure 2: Ledge image (top-left), line/edge detection (top-right), keypoints (bottom-
left) and disparity (bottom-right). See text.
but three directions are still missing (encircled). Here the structures have a size of 2 to
4 pixels: we are at the limit of what can be achieved by using Gabor wavelets.
Figure 2 shows, apart from line/edge and keypoint detection, disparity estimation
(bottom-right). Event types (top-right) are coded by different gray levels, and distance
in Î (bottom-right) as well. Disparity was obtained by shifting left, in one image of a
pair, the first vertical edge 3 pixels, the following edge 2, the next edges 1 pixel. The
second-last edge was not changed, and the last was shifted right. The lines and ring
were shifted left 1 pixel. As can be seen, disparity estimates are proportional to the
shifts, but there are still problems at keypoints. In addition, a comparison with tradi-
tional methods and experiments with real images showed that the interval ÏRÐÑ&Ò of the
filters is too small, even of the biggest filters. The reason is that these filters are the
smallest ones in the frequency domain. This is being solved by creating bigger filters,
5
doing the filtering by convolution in the spatial domain. The main conclusion is that it
will be possible to create a sort of “wireframe” representation in which lines and edged
are tagged with disparity, simplifying 3D object recognition. The same might occur in
our visual cortex.
Acknowledgement Part of this research is supported by ISR/IST in Lisbon, FCT Pro-
grama Operacional Sociedade de Informac¸a˜o (POSI) in the framework QCA III.
References
Deemter, J. v. and du Buf, J. (1996). Simultaneous detection of lines and edges using compound
Gabor filters. Int. J. of Pattern Recognition and Artificial Intelligence, 14(6):757–777.
du Buf, J. (1993). Responses of simple cells: events, interferences, and ambiguities. Biological
Cybernetics, 68:321–333.
Fleet, D. J., Jepson, A. D., and Jenkin, M. R. (1991). Phase-based disparity measurement.
CVGIP: Image Understanding, 53:198–210.
Heitger, F., Rosenthaler, L., von der Heydt, R., Peterhans, E., and Ku¨bler, O. (1992). Simulation
of neural contour mechanisms: from simple to end-stopped cells. Vis. Res., 32:963–981.
Hubel, D. H. (1995). Eye, brain and vision. Scientific American Library.
Ohzawa, I., DeAngelis, G. C., and Freeman, R. D. (1997). Encoding of binocular disparity by
complex cells in the cat’s visual cortex. J. Neurophysiol., 18(77):2879–2909.
Petkov, N. and Kruizinga, P. (1997). Computational models of visual neurons specialised in the
detection of periodic and aperiodic visual stimuli. Biological Cybernetics, 76(2):83–96.
Qian, N. (1997). Binocular disparity and the perception of depth. Neuron, 18:359–368.
Wu¨rtz, R. and Lourens, T. (1997). Corner detection in color images by multiscale combination
of end-stopped cortical cells. Artificial Neural Networks – ICANN’97, Springer LNCS Vol.
1327:901–906.
6


A vision fronted with a new disparity model

Sapientia (Univ. do Algarve)

A VISION FRONTEND WITH A NEW DISPARITYMODELJoa˜o Rodrigues and J.M. Hans du BufUniversity of Algarve, Faro, Portugaljrodrig@ualg.pt dubuf@ualg.ptAbstractWe are developing a frontend that is based on the image representation in thevisual cortex and plausible processing schemes. This frontend consists of multi-scale line/edge and keypoint (vertex) detection, using models of simple, complexand end-stopped cells. This frontend is being extended by a new disparity model.Assuming that there is no neural inverse tangent operator, we do not exploit Ga-bor phase information. Instead, we directly use simple cell (Gabor) responses atpositions where lines and edges are detected.1 IntroductionDuring the last decade, the modeling of processes in the visual cortex has becomea mature research topic. Mostly on the basis of Gabor quadrature filters as a modelof simple cells, models of complex cells and end-stopped cells have been developed,e.g. (Heitger et al., 1992). In addition, models for line/edge detection (Deemter anddu Buf, 1996) and bar and grating cells (Petkov and Kruizinga, 1997) have becomeavailable. Hence, it is now possible to develop a vision frontend that integrates all typesof processing and that can be used to explore higher-level tasks like object recognition.Because of the ocular dominance columns in the primary cortex (Hubel, 1995),which bring retinotopic, orientation-specific projections of the left and right eye closelytogether such that neural dendritic fields can cover both, we can assume that disparityestimation is already done in, or starts at, the first layers. However, we do not yetknow how this is done (Qian, 1997). One approach in computer vision is based onthe derivative of the local Gabor phase, also called the instantaneous frequency (Fleetet al., 1991). This method needs a coarse-to-fine scale stabilization and has problemsin regions where the Gabor amplitude is very small, but it can provide a very richand continuous disparity estimate. The Ohzawa-type model (Ohzawa et al., 1997)also employs quadrature Gabor filters, but it is more straightforward because disparity-sensitive complex cells are modeled by summing the squared responses of disparity-sensitive simple cells, the latter combining (positive) on and off Gabor responses ofthe left and right images. However, this model is still rather “academic” because it hasnot been tested with real images (the most complex example tested was a random dotstereogram, showing a very unstable disparity at the border, see (Qian, 1997)). It islikely that the Ohzawa-type model also needs a lot of postprocessing before it can beapplied to real images.Instead of experimenting with the Ohzawa-type model and the necessary stabiliza-tion, we decided to explore an alternative that is not based on phase nor amplitudesummations. The basic idea is extremely simple: once we have line/edge detection, wehave also access to the central, linear part of the Gabor responses, i.e. the sinusoidal orimaginary response in the case of lines and the sinusoidal-like or real response in the1case of an edge. Below we first introduce the basic keypoint and line/edge extractionwith the necessary stabilizations, and then the new disparity model.2 Lines, edges and keypointsLine, edge and keypoint detection are based on the responses of simple, complex andend-stopped cells. Gabor filters provide a simple model of cortical simple cells. In thespatial domain they consist of a real cosine and an imaginary sine, both with a Gaussianenvelope. Since all filtering is done in the frequency domain, we apply polar-separabletransfer functions  	ﬀﬁ	ﬂﬃ! #"ﬀ$&% '!()*+,! #"ﬀ$&% -/.with 013242326587:9and ;14242325=<>?9,%' and%- being the bandwidths in the frequencyand orientation, and5=<and587the number of scales and orientations. We apply alinear scaling between/@BA Cand/@BD6E, with the possibility of using many contiguousscales or a few noncontiguous scales with neighboring micro-scales, see below. Weuse5=7FHG.In the spatial domain, the responses of even and odd simple cells, which correspondto the real and imaginary parts of the Gabor filters, are denoted by IKJ<  MLNOPandIRQ< LN6OPTSbeing the scale and 0 the orientation (i.e. U RV   and U   0,W "	587X9 ). In order to simplify the notation, and because the same processing is done at allscales, we drop the subscriptS. The responses of complex cells are modelled by themodulus YMLNOPZ\[^]IJMLNOP`_ a]IQLNOb_ cde. There are two types of end-stopped cells (Heitger et al., 1992; Wu¨rtz and Lourens, 1997) , i.e. single (S) anddouble (D). Introducing f #Hghi U  and j #kilnm U  , these cells are modelled byop6LN6OPqr[YsMLautj6OKtf,vYMLtj6OawtfxcMyzML#6OP{}|YML#6OP~9$YLa$tj6O8ﬃ$tf~9$YMLﬃ$tj6Oa$tfyin which[cy denotes the suppression of negative values. The distance t is scaledlinearly with the filter scaleS, i.e. t12 S. All end-stopped responses along straightlines and edges need to be suppressed, for which we use tangential (T) and radial (R)inhibition:LN6OPq ~4pŁnp[Y@Bb~LNOaY@BbvMLawtf66OautjcyLN6OPq svpŁnp|Y@BbML#6OP~Yyvss @Bb~MLat$f6Oat$jxywhere0a57"&$Nh57V0h57. Instead of applying the inhibition to individ-ual end-stopped cells (Heitger et al., 1992; Wu¨rtz and Lourens, 1997), slightly betterresults are obtained by applyingaonce to the pooled activity:LNO>~ŁpopsML#6OP~+ML#6OPand LN6OPqv4Łpz6LN6OP~+LN6OP2with ¡+¢¤£¦¥ § , after which the keypoint map is obtained: ¨?©MªN«¬P­¯®±°³²&´Tµ¶¨ﬃ·N©MªN«¬P­b«¨ ¸R©ªN«6¬P­b¹« i.e. at each filter scale º : ¨¼»¶©MªN«¬P­ .Postprocessing of ¨?©Mª#«6¬P­ is necessary because our goal is to obtain a clean, single-pixel keypoint map with no spurious points. In addition, for pattern recognition appli-cations we want to classify the keypoints according to the underlying vertex structure,i.e. K, L, T, + etc. Postprocessing is done in six steps, at each scale, after which dif-ferent scales are combined by considering, around each scale, a small scale interval: 4micro-scales, i.e. two scales slightly finer and two slightly coarser than the actual scale.In the case of the smallest (largest) scale four coarser (finer) scales are applied. Onlykeypoints which are consistent over 3 neighboring micro-scales are accepted.Line and edge detection is based on simple cells (Deemter and du Buf, 1996).A positive line is detected where ½*¾ shows a local maximum and ½*¿ shows a zerocrossing. In the case of an edge the even and odd responses must be swapped. Thisgives 4 possibilities for positive and negative events: local maxima/minima plus zerocrossings. We also combine the responses of simple and complex cells, i.e. the simplecells serve to detect positions and event types, whereas the complex cells are used toincrease the confidence. Since the use of Gabor modulus (complex cells) implies a lossof precision at vertices (du Buf, 1993) we increase precision by considering multiplescales. Our improved detection scheme consists of 5 processing steps for each scale,after which the coherence is improved by checking 4 neighboring micro-scales.3 Disparity estimationOur disparity model is based on the central, linear part of the Gabor responses, i.e.the sinusoidal part with ÀÁnÂÃªw¢±ª#«Ä ªvÄvÅÇÆ#È¶§ . Assuming ideal events, i.e. lines witha Dirac profile and edges with a Heaviside step profile, or nonideal ones obtained byGaussian filtering, and complex Gabor filters with the same orientation, the responsesare (scaled) Gabor functions and complex errorfunctions. The latter can be approxi-mated by scaled Gabor functions (du Buf, 1993). In other words, both line and edgeresponses are essentially scaled Gabor functions. One step in line/edge detection con-sists of checking the Gabor response ½*¿É ©Mª#«6¬P­ (the odd, imaginary part in the case ofa line), or ½R¾É ©Mª#«6¬P­ (the even, real (!) part in the case of an edge) for a zero crossingon ÊRËÌÈ¶§ . Here, for disparity, we apply the same event detection steps to two images,left and right. In the case of the left image, we (1) check the existence of an event ofthe same type in the right image on ÊRËÈ&Í , and (2) if so, we take the value of Ê¯½ ¿ orÊ¯½R¾ of the right image at the event (zero crossing) position in the left image. The signdepends on the event polarity and, in order to obtain values which do not depend onthe event amplitude, Ê¯½R¿ or Ê¯½R¾ is divided by the modulus (complex cell response)of the left image, which is maximum at the event position. After this normalization yetanother one is applied: the response is divided by the scale º of the filter. Hence, theslope of the linear response part will not depend on the event amplitude nor on the filterscale, i.e. disparity estimates obtained at different scales will be the same. The sameprocessing can be done in the case of the right image, by exchanging left and right. Ofcourse, the disparity estimates need to be calibrated once using real data, like the waybabies need to learn in the first months.3Figure 1: Top: sign2 image and line/edge detection. Bottom: keypoints detected withevent directions, after multi-scale stabilization (zoomed).One problem we encountered were small fluctuations of the disparity estimates,especially at the finest scales. These are due to the fact that we need to work at discretepixel positions, and the maximum of the modulus used in the first normalization istherefore not the theoretical maximum. We solved this by averaging disparity estimatesover neighboring scales.4 Results and discussionFigure 1 shows results of line/edge and keypoint detection. Single- and multi-scalestabilization has eliminated many spurious keypoints, one of which is shown by thesmall diamond of 4 pixels (bottom image). All keypoints of the van have been detected,4Figure 2: Ledge image (top-left), line/edge detection (top-right), keypoints (bottom-left) and disparity (bottom-right). See text.but three directions are still missing (encircled). Here the structures have a size of 2 to4 pixels: we are at the limit of what can be achieved by using Gabor wavelets.Figure 2 shows, apart from line/edge and keypoint detection, disparity estimation(bottom-right). Event types (top-right) are coded by different gray levels, and distancein Î (bottom-right) as well. Disparity was obtained by shifting left, in one image of apair, the first vertical edge 3 pixels, the following edge 2, the next edges 1 pixel. Thesecond-last edge was not changed, and the last was shifted right. The lines and ringwere shifted left 1 pixel. As can be seen, disparity estimates are proportional to theshifts, but there are still problems at keypoints. In addition, a comparison with tradi-tional methods and experiments with real images showed that the interval ÏRÐÑ&Ò of thefilters is too small, even of the biggest filters. The reason is that these filters are thesmallest ones in the frequency domain. This is being solved by creating bigger filters,5doing the filtering by convolution in the spatial domain. The main conclusion is that itwill be possible to create a sort of “wireframe” representation in which lines and edgedare tagged with disparity, simplifying 3D object recognition. The same might occur inour visual cortex.Acknowledgement Part of this research is supported by ISR/IST in Lisbon, FCT Pro-grama Operacional Sociedade de Informac¸a˜o (POSI) in the framework QCA III.ReferencesDeemter, J. v. and du Buf, J. (1996). Simultaneous detection of lines and edges using compoundGabor filters. Int. J. of Pattern Recognition and Artificial Intelligence, 14(6):757–777.du Buf, J. (1993). Responses of simple cells: events, interferences, and ambiguities. BiologicalCybernetics, 68:321–333.Fleet, D. J., Jepson, A. D., and Jenkin, M. R. (1991). Phase-based disparity measurement.CVGIP: Image Understanding, 53:198–210.Heitger, F., Rosenthaler, L., von der Heydt, R., Peterhans, E., and Ku¨bler, O. (1992). Simulationof neural contour mechanisms: from simple to end-stopped cells. Vis. Res., 32:963–981.Hubel, D. H. (1995). Eye, brain and vision. Scientific American Library.Ohzawa, I., DeAngelis, G. C., and Freeman, R. D. (1997). Encoding of binocular disparity bycomplex cells in the cat’s visual cortex. J. Neurophysiol., 18(77):2879–2909.Petkov, N. and Kruizinga, P. (1997). Computational models of visual neurons specialised in thedetection of periodic and aperiodic visual stimuli. Biological Cybernetics, 76(2):83–96.Qian, N. (1997). Binocular disparity and the perception of depth. Neuron, 18:359–368.Wu¨rtz, R. and Lourens, T. (1997). Corner detection in color images by multiscale combinationof end-stopped cortical cells. Artificial Neural Networks – ICANN’97, Springer LNCS Vol.1327:901–906.6

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A vision fronted with a new disparity model

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