chapter 9 conclusions and future workstrider/publications/chapter9.pdf · chapter 9 conclusions and...

Chapter 9

Conclusions and Future Work

In this work we have explored the problem of bottom-up figure-ground segmentation, both as

an image segmentation task, and as a perceptual grouping problem. We presented an compre-

hensive overview of current research in both fields, and discussed reasons why despite a vast

research effort, image segmentation and perceptual grouping on unconstrained images continue

to be extremely challenging.

Up to this point, we have not discussed the relationship between image segmentation and

perceptual grouping. It is clear from our research, that our current implementations of each of

these methodologies are particularly well suited to certain classes of images. Our contour ex-

traction algorithm can be expected to yield good results in reasonably structured environments,

and on images that contain simple objects. SE-MinCut proves particularly useful for dealing

with less structured environments, and with irregularly shaped objects. Figure 9.1 illustrates

some of these points.

Image segmentation and perceptual grouping have traditionally relied on different image

cues. Segmentation is often based mostly on pixel appearance, be it by using brightness, colour,

or some measure of texture similarity (though the issue of cue integration for segmentation has

received a reasonable amount of attention, see [62, 63]); whereas perceptual grouping usually

relies on the information provided by image edges, and on grouping principles that exploit the

190

CHAPTER 9. CONCLUSIONS AND FUTURE WORK 191

Figure 9.1: Two images with different characteristics, and results from SE-MinCut, and our

contour extraction method. Notice that on the top image which comes from a structured en-

vironment, contour extraction performs particularly well. Conversely, on the bottom image,

which comes from a relatively un-structured environment, SE-MinCut works best. In gen-

eral, contour extraction using only edge information is not well suited for un-structured envi-

ronments, or objects whose boundaries are too irregular. It should be noted that SE-MinCut

performed segmentation on downsampled versions of each image.


regularities among edges that belong to object contours.

The information provided by image segmentation and perceptual grouping is also comple-

mentary. Segmentation results indicate what regions in the image look homogeneous under

a chosen similarity measure, without considering boundary regularity; while grouping results

indicate which edges in the image form regular groups that are likely to correspond to salient

boundaries. It is reasonable to expect that combining the results produced by segmentation and

grouping should lead to better figure-ground segmentation.

In our particular case, we have shown quantitative evidence that the SE-MinCut algorithm

is able to capture a large percentage of the boundary structure that human observers considered

salient across a large image database. However, we noted that capturing more of the salient

image structure resulted in additional over-segmentation, and that a merging stage would be

required to join together image regions that are likely to belong to single objects. Furthermore,

we pointed out that such a merging stage would have to rely on cues other than pixel appear-

ance. This suggests that image segmentation would benefit from a merging stage based on

perceptual grouping principles that group regions together, so as to achieve boundaries with

the desired properties (smoothness, compactness, symmetry, etc.).

We have also shown that our contour extraction algorithm can be biased using additional

image cues, and demonstrated the improved results obtained by incorporating simple colour

information into the search framework. We expect that region information could be used in a

similar way to provide additional guidance for the grouping method. In particular, region infor-

mation could be used to bias the grouping procedure so that it avoids grouping with segments

that are contained in regions that have already been determined to be homogeneous by the im-

age segmentation algorithm. This would be particularly useful in heavily textured regions of

the image.

By preferentially following paths in the image that have been marked as boundaries by the

segmentation algorithm, the grouping stage would in effect be performing the task of deciding

which regions output by the segmentation algorithm should be merged, based on the percep-


tual grouping principles used by the contour extraction method. We have reason to believe that

such a scheme would provide better figure-ground segmentation results than either image seg-

mentation of contour extraction alone. The integration of image segmentation and perceptual

grouping results is potentially the most beneficial direction for future research.

Other future research directions include the improvement of the SE-MinCut algorithm to

use a more comprehensive measure of the affinity between pixels. We can also improve the

algorithm that generates source/sink combinations for Min-Cut so as to reduce the number of

cuts that have to be performed on larger images, with the subsequent increase in performance.

It would be worthwhile to enhance the merging stage to increase robustness, and decrease the

likelihood of under-segmentation. Another potentially beneficial extension would be to modify

the SE-MinCut algorithm to perform recursive, coarse-to-fine segmentation, thereby achieving

better performance, and allowing the algorithm to segment higher-resolution images.

The contour extraction algorithm can be extended to find and remove paths that lead only

to open chains; it can also be adapted to perform grouping at multiple scales, and then use

grouping results at coarser levels to bias the search at finer levels. Another interesting possibil-

ity is to have the algorithm find small contour fragments (of at most a few segments, which can

be done quite efficiently), and then combine partial chains into contours. This should be more

efficient than performing the deeper search required to extract full contours, and doing this for

every image segment. Finally, there remains the issue of defining a robust, general measure of

contour saliency. Though our current saliency measures perform well, we expect that as more

image information becomes available (e.g. by incorporating image segmentation results) the

ranking of output contours can be enhanced.

9.1 Summary of Contributions

In this thesis, we have made contributions to the fields of image segmentation and perceptual

grouping. Within the field of image segmentation, we have presented spectral embedding as


a general technique for clustering data. We have shown a direct connection between spectral

embedding and anisotropic, smoothing kernels. We’ve used spectral embedding to generate

seed regions for min-cut, proposed an algorithm for combining seed regions into source/sink

pairs, and shown that the resulting partitions capture salient image structure.

We proposed a complete segmentation algorithm, and showed a visual comparison of seg-

mentation results between SE-MinCut and three of the leading segmentation algorithms. We

also carried out a thorough quantitative evaluation of segmentation quality over the Berkeley

Segmentation Database. We proposed a suitable algorithm for matching the boundaries of

two segmentations, and used precision/recall metrics based on this boundary matching to mea-

sure segmentation quality. Our results indicate that SE-MinCut produces better segmentations

across its range of input parameters, in particular, SE-MinCut is capable of capturing a higher

fraction of the salient boundaries of an image with less over-segmentation than competing al-

gorithms, and the boundaries themselves are more accurately localized.

In the field of perceptual grouping, we presented a robust and efficient search framework for

contour extraction. Our framework is based on locally normalized, pairwise affinities between

line segments, and includes a search control technique to keep the algorithm from repeatedly

finding variations of the same shape. We demonstrated the algorithm first in the domain of

convex group detection, where we showed that the use of normalized affinities resulted in

robust performance on line sets with significant variation. We demonstrated that a single set of

parameters yields excellent performance on all our test images, and that the algorithm achieves

a reduction of several orders of magnitude in search complexity with regard to a previous

method for convex group extraction, based on boundary coverage.

We then presented a general contour extraction procedure based on our search framework.

Our contour extraction algorithm uses compactness and smooth continuation as grouping con-

straints, and achieves a similar level of performance as our convex group detector. We showed

experimental results on a variety of images, all of which indicate that the framework can ef-

ficiently and robustly detect salient image contours. Finally, we demonstrated the flexibility


of the search framework by incorporating colour information during the search phase, as well

as for evaluating the saliency of the extracted contours. The resulting algorithm can deal with

heavily textured objects, and the resulting contours agree much better with the observed im-

age structure. Our algorithm performs contour extraction efficiently on images in which the

abundance of clutter, texture, and repeated structure makes other current grouping algorithms

impractical.

We believe that both the SE-MinCut algorithm, and our contour extraction method rep-

resent significant advances in their corresponding fields. The work presented in this thesis

demonstrates that bottom-up figure-ground segmentation can be pushed a long way for arbi-

trary images. Though there remains a significant amount of work to be done before the figure-

ground discrimination problem is solved, we believe that bottom-up algorithms are close to the

point where they can be used as a practical pre-processing stage for higher level vision tasks

such as object recognition and tracking.

Bibliography

[1] Arnon Amir and Michael Lindenbaum. A generic grouping algorithm and its quan-

titative analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence,

20(3):168–186, February 1998.

[2] Adrian Barbu and Song-Chun Zhu. Graph partition by Swendsen-Wang cuts. In IEEE

International Conference on Computer Vision, pages 320–327, 2003.

[3] M. Belkin and P. Niyogi. Laplacian eigenmaps and spectral techniques for embedding

and clustering. In ”T.G. Diettrich, S. Becker, and Z. Ghahramani”, editors, ”Adv. in

Neural Inf. Proc. Sys. 14”, pages 585–591. MIT Press, 2002.

[4] Serge Belongie, Charless Fowlkes, Fan Chung, and Jitendra Malik. Spectral partition-

ing with indefinite kernels using the Nystrom extension. In European Conference on

Computer Vision, pages 21–31, 2002.

[5] Serge Belongie and Jitendra Malik. Finding boundaries in natural images: A new

method using point descriptors and area completion. In European Conference on Com-

puter Vision, pages 751–766, 1998.

[6] J. Ross Beveridge, Joey Griffith, Ralf R. Kohler, Allen R Hanson, and Edward M Rise-

man. Segmenting images using localized histograms and region merging. International

Journal of Computer Vision, 2(3):311–347, jan. 1989.

[7] C. M. Bishop. Neural Networks for Pattern Recognition. Oxford Univ. Press, 1995.

196

BIBLIOGRAPHY 197

[8] A. Blake, A. Rother, M. Brown, P. Perez, and P. Torr. Interactive image segmentation

using an adaptive GMMRF model. In European Conference on Computer Vision, pages

428–441, 2004.

[9] Sudhir Borra and Sudeep Sarkar. A framework for performance characterization of

intermediate-level grouping modules. IEEE Transactions on Pattern Analysis and Ma-

chine Intelligence, 19(11):1306–1312, November 1997.

[10] Kim L. Boyer and Sudeep Sarkar. Perceptual Organization for Artificial Vision Systems.

Kluwer Academic Publishers, 2000.

[11] Yuri Boykov and Vladimir Kolmogorov. An experimental comparison of min-cut/max-

flow algorithms for energy minimization in vision. In International Workshop on Energy

Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in

Computer Science, pages 359–374, 2001.

[12] Yuri Boykov, Olga Veksler, and Ramin Zabih. Fast approximate energy minimiza-

tion via graph cuts. IEEE Transactions on Pattern Analysis and Machine Intelligence,

23(11):1222–1239, 2001.

[13] Yuri Y. Boykov and Marie-Pierre Jolly. Interactive Graph Cuts for optimal boundary

& region segmentation of objects in N-D images. In IEEE International Conference on


[14] Matthew Brand and Kun Huang. A unifying theorem for spectral embedding and cluster-

ing. Technical Report TR-2002-42, MERL - A Mistubishi Electric Research Laboratory,

nov. 2002.

[15] Amit Chakraborty, Lawrence H. Staib, and James S. Duncan. Deformable boundary

finding influenced by region homogeneity. In IEEE Conference on Computer Vision

and Pattern Recognition, pages 624–627, 1994.

BIBLIOGRAPHY 198

[16] Yizong Cheng. Mean shift, mode seeking, and clustering. IEEE Transactions on Pattern

Analysis and Machine Intelligence, 17(8):790–799, aug. 1995.

[17] Chakra Chennubhotla. Spectral Methods for Multi-Scale Feature Extraction and Data

Clustering. PhD thesis, University of Toronto, Department of Computer Science, 2004.

[18] Boris V. Cherkassky and Andrew A. Goldberg. On implementing push-relabel method

for the maximum flow problem. In International Conference on Integer Programming

and Combinatorial Optimization, pages 157–171, 1995.

[19] Kyujin Cho and Peter Meer. Image segmentation from consensus information. Com-

puter Vision and Image Understanding, 68(1):72–89, oct. 1997.

[20] David T. Clemens and David W. Jacobs. Space and time bounds on indexing 3-d models

from 2-d images. IEEE Transactions on Pattern Analysis and Machine Intelligence,

13(10):1007–1017, October 1991.

[21] D. Comaniciu and P. Meer. Robust analysis of feature spaces: Color image segmenta-

tion. In IEEE Conference on Computer Vision and Pattern Recognition, pages 750–755,

1997.

[22] D. Comaniciu and P. Meer. Mean shift analysis and applications. In IEEE International

Conference on Computer Vision, pages 1197–1203, 1999.

[23] Timothee Cour, Stella Yu, and Jianbo Shi. Normalized cuts matlab code.

Computer and Information Science, Penn State University. code available at

http://www.cis.upenn.edu/˜jshi/software/.

[24] James Elder and Steven Zucker. The effect of contour closure on the rapid discrimination

of two-dimensional shapes. Vision Research, (33):981–991, 1993.

BIBLIOGRAPHY 199

[25] James H. Elder, Amnon Krupnik, and Leigh A. Johnston. Contour grouping with prior

models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(6):661–

674, June 2003.

[26] James H. Elder and Steven W. Zucker. A measure of closure. Technical Report 93-2,

McGill Research Centre for Intelligent Machines, 1994.

[27] James H. Elder and Steven W. Zucker. Computing contour closure. In European Con-

ference on Computer Vision, pages 399–412, 1996.

[28] Pedro Felzenszwalb and Daniel Huttenlocher. Image segmentation by lo-

cal variation code. MIT Artificial Intelligence Lab. code available at

http://www.ai.mit.edu/people/pff/seg/seg.html .

[29] Pedro F. Felzenszwalb and Daniel P. Huttenlocher. Image segmentation using local

variation. In IEEE Conference on Computer Vision and Pattern Recognition, pages 98–

104, 1998.

[30] D. J. Field, A. Hayes, and R. F. Hess. Contour integration by the human visual system:

Evidence for a local ”association field”. Vision Research, (33):173–193, 1993.

[31] Bernd Fischer and Joachim M. Buhmann. Path-based clustering for grouping of smooth

curves and texture segmentation. IEEE Transactions on Pattern Analysis and Machine

Intelligence, 25(4):513–518, April 2003.

[32] L. R. Ford and E. Fulkerson. Flows in Networks. Princeton University Press, Princeton,

N.J., 1962.

[33] Charless Fowlkes, Serge Belongie, Fan Chung, and Jitendra Malik. Spectral grouping

using the Nystrom method. IEEE Transactions on Pattern Analysis and Machine Intel-

ligence, 26(2):214–225, 2004.

BIBLIOGRAPHY 200

[34] Charless Fowlkes, Serge Belongie, and Jitendra Malik. Efficient spatiotemporal group-

ing using the Nystrom method. In IEEE Conference on Computer Vision and Pattern

Recognition, pages 231–238, 2001.

[35] Charless Fowlkes, David Martin, and Jitendra Malik. Learning affinity functions for

image segmentation: Combining patch-based and gradient-based approaches. In IEEE

Conference on Computer Vision and Pattern Recognition, pages 54–61, 2003.

[36] Yoram Gdalyahu, Daphna Weinshall, and Michael Werman. Self-organization in vi-

sion: Stochastic clustering for image segmentation, perceptual grouping, and image

database organization. IEEE Transactions on Pattern Analysis and Machine Intelli-

gence, 23(10):1053–1074, oct. 2001.

[37] Bogdan Georgescu and Chris M. Christoudias. The Edge Detection and Image segmen-

tatiON (EDISON) system. Robust Image Understanding Laboratory, Rutgers University.

code available at http://www.caip.rutgers.edu/riul/research/code.html .

[38] R. E. Gomory and T. C. Hu. Multi-terminal network flows. SIAM Journal of Applied

Mathematics, 9:551–570, 1961.

[39] W. Eric L. Grimson. The combinatorics of heuristic search termination for object recog-

nition in cluttered environments. IEEE Transactions on Pattern Analysis and Machine

Intelligence, 13(9):920–935, September 1991.

[40] Gideon Guy and Gerard Medioni. Inferring global perceptual contours from local fea-

tures. International Journal of Computer Vision, 20(1/2):113–133, 1996.

[41] Gideon Guy and Gerard Medioni. Inference of surfaces, 3d curves, and junctions from

sparse, noisy, 3d data. IEEE Transactions on Pattern Analysis and Machine Intelligence,

19(11):1265–1277, November 1997.

BIBLIOGRAPHY 201

[42] Robert M. Haralick and Linda G. Shapiro. Image segmentation techniques. Computer

Vision, Graphics and Image Processing, 29(1):100–132, jan. 1985.

[43] Matthias Heiler and Christoph Schnorr. Natural image statistics for natural image seg-

mentation. In IEEE International Conference on Computer Vision, pages 1259–1266,

2003.

[44] Berthold K. P. Horn. Robot Vision. MIT Press, Cambridge, 1986.

[45] Daniel P. Huttenlocher and Peter C. Wayner. Finding convex edge groupings in an

image. International Journal of Computer Vision, 8(1):7–27, July 1992.

[46] Hiroshi Ishikawa and Davi Geiger. Segmentation by grouping junctions. In IEEE Con-

ference on Computer Vision and Pattern Recognition, pages 125–131, 1998.

[47] David W. Jacobs. Robust and efficient detection of salient convex groups. IEEE Trans-

actions on Pattern Analysis and Machine Intelligence, 18(1):23–37, January 1996.

[48] Allan D. Jepson and Richard Mann. Qualitative probabilities for image interpretation.

In IEEE International Conference on Computer Vision, volume 2, pages 1123–1130,

1999.

[49] Ian H. Jermyn and Hiroshi Ishikawa. Globally optimal regions and boundaries. In IEEE


[50] Leigh A. Johnston and James H. Elder. Efficient computation of closed contours using

modified Baum-Welch updating. In IEEE Workshop on Perceptual Organization in

Computer Vision, 2004.

[51] Timothy N. Jones and Dimitris N. Metaxas. Image segmentation based on the integration

of pixel affinity and deformable models. In IEEE Conference on Computer Vision and

Pattern Recognition, pages 330–337, 1998.

BIBLIOGRAPHY 202

[52] Timor Kadir and Michael Brady. Unsupervised non-parametric region segmentation

using level sets. In IEEE International Conference on Computer Vision, pages 1267–

1274, 2003.

[53] David R. Karger and Clifford Stein. A new approach to the minimum cut problem.

Journal of the ACM, 43(4):601–640, 1996.

[54] Michael Kass, Andrew Witkin, and Demetri Terzopoulos. Snakes: Active contour mod-

els. International Journal of Computer Vision, 1(4):321–331, 1988.

[55] J. R. Kemeny and J. L. Snell. Finite Markov Chains. Van Nostrand, 1960.

[56] K. Koffka. Principles of Gestalt Psychology. Harcourt, Brace, & World, New York,

1935.

[57] P. Kornprobst and G. Medioni. Tracking segmented objects using tensor voting. In

IEEE Conference on Computer Vision and Pattern Recognition, volume 2, pages 118–

125, 2000.

[58] David G. Lowe. Perceptual Organization and Visual Recognition. Kluwer Academic

Publishers, Boston, MA, 1985.

[59] David G. Lowe. Three-dimensional object recognition from single two-dimensional

images. Artificial Intelligence, 31(3):355–395, March 1987.

[60] Shyjan Mahamud, Karvel K. Thornber, and Lance R. Williams. Segmentation of salient

closed contours from real images. In IEEE International Conference on Computer Vi-

sion, pages 891–897, 1999.

[61] Shyjan Mahamud, Lance R. Williams, Karvel K. Thornber, and Kanglin Xu. Segmenta-

tion of multiple salient closed contours from real images. IEEE Transactions on Pattern

Analysis and Machine Intelligence, 25(4):433–444, April 2003.

BIBLIOGRAPHY 203

[62] Jitendra Malik, Serge Belongie, Thomas Leung, and Jianbo Shi. Textons, contours and

regions: Cue integration in image segmentation. In IEEE International Conference on


[63] Jitendra Malik, Serge Belongie, Thomas Leung, and Jianbo Shi. Contour and texture

analysis for image segmentation. International Journal of Computer Vision, 43(1):7–

27, 2001.

[64] David Martin. An Empirical Approach to Grouping and Segmentation. PhD thesis,

University of California, Berkeley, 2002.

[65] David Martin and Charless Fowlkes. The Berkeley segmentation database

and benchmark. Computer Science Department, Berkeley University.

http://www.cs.berkeley.edu/projects/vision/grouping/segbench/.

[66] David Martin, Charless Fowlkes, Doron Tal, and Jitendra Malik. A database of human

segmented natural images and its application to evaluating segmentation algorithms and

measuring ecological statistics. In IEEE International Conference on Computer Vision,

pages 416–425, 2001.

[67] David R. Martin, Charless C. Fowlkes, and Jitendra Malik. Learning to detect natu-

ral image boundaries using brightness and texture. In Neural Information Processing

Systems, 2002.

[68] Tim McInerny and Demetri Terzopoulos. Deformable models in medical image analysis:

a survey. Medical Image Analysis, 1(2):91–108, 1996.

[69] Tim McInerny and Demetri Terzopoulos. T-snakes: Topology adaptive snakes. Medical

Image Analysis, 4(2):73–91, 2000.

BIBLIOGRAPHY 204

[70] Gerard Medioni, Mi-Suen Lee, and Chi-Keung Tang. Tensor voting download page.

Institute for Robotics and Intelligent Systems, University of Southern California. code

available at http://iris.usc.edu/˜tensorvt/ .

[71] Marina Meila and Jianbo Shi. Learning segmentation by random walks. In NIPS, pages

873–879, 2000.

[72] C. D. Meyer. Matrix Analysis and Applied Linear Algebra. Society for Industrial and

Applied Mathematics, 2000.

[73] E. Mingolla, W. Ross, and S. Grossberg. A neural ntwork for enhancing boundaries and

surfaces in synthetic aperture radar images. Neural Networks, 12:499–511, 1999.

[74] Rakesh Mohan and Ramakant Nevatia. Segmentation and description based on percep-

tual organization. In IEEE Conference on Computer Vision and Pattern Recognition,

pages 333–341, 1989.

[75] Rakesh Mohan and Ramakant Nevatia. Perceptual organization for scene segmenta-

tion and description. IEEE Transactions on Pattern Analysis and Machine Intelligence,

14(6):616–635, June 1992.

[76] David Mumford. Algebraic Geometry and its Applications, chapter Elastica and Com-

puter Vision. Springer-Verlag, N.Y., 1994.

[77] Heiko Neumann and Ennio Mingolla. Computational neural models of spatial integra-

tion in perceptual grouping. In T. Shipley and P. Kellman, editors, From fragments to

units: Segmentation and grouping in vision, pages 353–400. Elsevier Science, Oxford,

UK, 2001.

[78] Andrew Y. Ng, Michael I. Jordan, and Yair Weiss. On spectral clustering: Analysis and

an algorithm. In Advances in Neural Information Processing Systems 14, 2002.

BIBLIOGRAPHY 205

[79] Mark Nitzberg and David Mumford. The 2.1-D sketch. In IEEE International Confer-

ence on Computer Vision, pages 138–144, 1990.

[80] Nikhil R. Pal and Sankar K. Pal. A review on image segmentation techniques. Pattern

Recognition, 26(9):1277–1294, 1993.

[81] Hsing-Kuo Pao, Davi Geiger, and Nava Rubin. Measuring convexity for figure/ground

separation. In IEEE International Conference on Computer Vision, pages 948–955,

1999.

[82] Nikos Paragios. Geodesic Active Regions and Level Set Methods: Contributions and

Applications in Artificial Vision. PhD thesis, University of Nice/Sophia Antipolis, jan.

2000.

[83] Nikos Paragios and Rachid Deriche. Coupled geodesic active regions for image seg-

mentation: A level set approach. In European Conference on Computer Vision, pages

224–240, 2000.

[84] P. Perona and W. Freeman. A factorization approach to grouping. In European Confer-

ence on Computer Vision, pages 655–670, 1998.

[85] P. Perona and J. Malik. Scale-space and edge detection using anisotropic diffusion. IEEE

Transactions on Pattern Analysis and Machine Intelligence, 12(7):629–639, 1990.

[86] Xiaofeng Ren and Jitendra Malik. A probabilistic multi-scale model for contour com-

pletion based on image statistics. In European Conference on Computer Vision, pages

312–327, 2002.

[87] Xiaofeng Ren and Jitendra Malik. Learning a classification model for segmentation. In

IEEE International Conference on Computer Vision, pages 10–16, 2003.

BIBLIOGRAPHY 206

[88] Sudeep Sarkar and Kim L. Boyer. Automated design of bayesian perceptual inference

networks. Technical Report SAMPL-93-03, SAMPL-Lab, Department of Electrical En-

gineering, OSU, 1993.

[89] Sudeep Sarkar and Kim L. Boyer. Integration, inference, and management of spatial

information using bayesian networks: Perceptual organization. IEEE Transactions on

Pattern Analysis and Machine Intelligence, 15(3):256–274, March 1993.

[90] Sudeep Sarkar and Kim L. Boyer. Using perceptual inference networks to manage vision

processes. Computer Vision, Graphics, and Image Processing: Image Understanding,

62(1):27–46, July 1995.

[91] Sudeep Sarkar and Kim L. Boyer. Quantitative measures of change based on feature

organization: Eigenvalues and eigenvectors. In IEEE Conference on Computer Vision

and Pattern Recognition, pages 478–483, 1996.

[92] Sudeep Sarkar and Padmanabhan Soundararajan. Supervised learning of large percep-

tual organization: Graph spectral partitioning and learning automata. IEEE Transactions

on Pattern Analysis and Machine Intelligence, 22(5):504–525, 2000.

[93] Eric Saund. Finding perceptually closed paths in sketches and drawings. IEEE Trans-

actions on Pattern Analysis and Machine Intelligence, 25(4):475–491, 2003.

[94] Eitan Sharon, Achi Brandt, and Ronen Basri. Fast multiscale image segmentation. In

IEEE Conference on Computer Vision and Pattern Recognition, pages 70–77, 2000.

[95] Eitan Sharon, Achi Brandt, and Ronen Basri. Segmentation and boundary detection

using multiscale intensity measurements. In IEEE Conference on Computer Vision and

Pattern Recognition, pages 469–476, 2001.

BIBLIOGRAPHY 207

[96] Noam Shental, Assaf Zomet, Tomer Hertz, and Yair Weiss. Learning and inferring image

segmentations using the GBP typical cut algorithm. In IEEE International Conference

on Computer Vision, pages 1243–1250, 2003.

[97] Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. In IEEE


[98] Jianbo Shi and Jitendra Malik. Normalized cuts and image segmentation. IEEE Trans-

actions on Pattern Analysis and Machine Intelligence, 22(8):888–905, 2000.

[99] Lawrence H. Staib and James S. Duncan. Boundary finding with parametrically de-

formable models. IEEE Transactions on Pattern Analysis and Machine Intelligence,

14(11):1061–1075, nov. 1992.

[100] M. Swain and D. Ballard. Color indexing. International Journal of Computer Vision,

7(1):11–32, 1991.

[101] K. K. Thornber and L. R. Williams. Analytic solution of stochastic completion fields.

Biological Cybernetics, 75:141–151, 1996.

[102] Carlo Tomasi and Roberto Manduchi. Bilateral filtering for gray and color images. In


[103] Zhuowen Tu, Song-Chun Zhu, and Heung-Yeung Shum. Image segmentation by data

driven Markov chain monte carlo. In IEEE International Conference on Computer Vi-

sion, pages 131–138, 2001.

[104] Shimon Ullman and Amnon Sha’ashua. Structural saliency: The detection of globally

salient structures using a locally connected network. Technical Report A.I. Memo No.

1061, MIT, Artificial Intelligence Laboratory, 1988.

[105] Olga Veksler. Image segmentation by nested cuts. In IEEE Conference on Computer

Vision and Pattern Recognition, pages 339–344, 2000.

BIBLIOGRAPHY 208

[106] B. A. Wandell. Foundations of Vision. Sinauer Associates Inc., 1995.

[107] Song Wang, Toshiro Kubota, and Jeffrey Mark Siskind. Salient boundary detection

using ratio contour. In Neural Information Processing Systems Conference, 2003.

[108] Song Wang and Jeffrey M. Siskind. Image segmentation with minimum mean cut. In


[109] Song Wang and Jeffrey M. Siskind. Image segmentation with ratio cut. IEEE Transac-

tions on Pattern Analysis and Machine Intelligence, 25(6):675–690, 2003.

[110] Song Wang, Jun Wang, and Kubota Toshiro. From fragments to salient closed bound-

aries: An in-depth study. In IEEE Conference on Computer Vision and Pattern Recog-

nition, pages 291–298, 2004.

[111] Yair Weiss. Segmentation using eigenvectors: a unifying view. In IEEE International


[112] M. Wertheimer. A Sourcebook of Gestalt Psychology, chapter Laws of organization in

perceptual forms. Routledge and Kegan Paul, London. U.K., 1938.

[113] Lance R. Williams and David W. Jacobs. Stochastic completion fields: A neural model

of illusory contour shape and salience. Neural Computation, 9(4):837–858, May 1997.

[114] Lance R. Williams and Karvel K. Thornber. A comparison of measures for detecting

natural shapes in cluttered backgrounds. International Journal of Computer Vision,

34(2):81–96, 2000.

[115] A. P. Witkin and J. M. Tenenbaum. Human and Machine Vision, chapter On the role of

structure in vision, pages 481–543. Academic Press, 1983.

[116] Zhenyu Wu and Richard Leahy. An optimal graph theoretic approach to data cluster-

ing: Theory and its application to image segmentation. IEEE Transactions on Pattern

Analysis and Machine Intelligence, 15(11):1101–1113, nov. 1993.

BIBLIOGRAPHY 209

[117] Stella X. Yu and Jianbo Shi. Multiclass spectral clustering. In IEEE International


[118] Song-Chun Zhu. Region competition: Unifying snakes, region growing, and

Bayes/MDL for multi-band image segmentation. Technical Report 94-10, Harvard

Robotics Laboratory, 1994.

chapter 9 conclusions and future workstrider/publications/chapter9.pdf · chapter 9 conclusions and...

Documents