1  of  45  

Efficient  Globally  Op5mal  Consensus  Maximisa5on  with  Tree  Search  

Tat-­‐Jun  Chin  School  of  Computer  Science  The  University  of  Adelaide  

by  T.-­‐J.  Chin  

2  of  45  

Maximum  consensus  

by  T.-­‐J.  Chin  

max

✓, I✓X|I|

subject to ri(✓) ✏ 8xi 2 I,

3  of  45  

Example  1:  Line  fiMng  

by  T.-­‐J.  Chin  

4  of  45  

Example  2:  Triangula5on  

by  T.-­‐J.  Chin  

Fig. 5. The triangulation problem: Assuming that the maximum reprojection erroris less than some value �, the sought point X must lie in the intersection of a set ofcones. If � is set too small, then the cones do not have a common intersection (left). If� is set too large, then the cones intersect in a convex region in space, and the desiredsolution X must lie in this region (right). The optimal value of � lies between thesetwo extremes, and can be found by a binary search (bisection) testing successive valuesof �. For more details, refer to the text.

2. If we define a cost function

Cost1(X) = maxi

\(X�Oi,vi) ,

then the sublevel set S�(Cost1) is simply the intersection of the conesC�(Oi,vi), which is convex for all �. This by definition says that Cost1(X)is a quasi-convex function of X.

3. Finding the optimum

minX

Cost1(X) = minX

maxi

\(X�Oi,vi)

is accomplished by a binary search over possible values of �, where for eachvalue of � we solve an SOCP feasibility problem, (determine whether a set ofcones have a common intersection). Such a problem is known as a minimaxor L1 optimization problem.

Generally speaking, this procedure generalizes to arbitrary quasi-convex op-timization problems; they may be solved by binary search involving a convexfeasibility problem at each step. If we have a set of individual cost functionsfi(X), perhaps each associated with a single measurement, and each of themquasi-convex, then the maximum of these cost functions maxi fi(X) is also quasi-convex, as illustrated in Fig 4. In this case, the minimax problem of findingminX maxi fi(X) is solvable by binary search.

Reconstruction with known rotations. Another problem that may besolved by very similar means to the triangulation problem is that of Structureand Motion with known rotations, which is illustrated in Fig 6.

Figure 3. Two images from the dinosaur sequence, and the resulting reconstruction.

Figure 4. Two images from the house sequence, and the resulting reconstruction.

Figure 5. Two images from the church sequence, and the resulting reconstruction.

[15] Y. Seo, H. Lee, and S. W. Lee. Outlier removal by convexoptimization for l-infinity approaches. In PSIVT ’09: PacificRim Symposium on Advances in Image and Video Technol-ogy, 2009.

[16] K. Sim and R. Hartley. Removing outliers using the L1-norm. In Conf. Computer Vision and Pattern Recognition,pages 485–492, New York City, USA, 2006.

[17] H. Stewenius, C. Engels, and D. Nister. Recent develop-

ments on direct relative orientation. ISPRS Journal of Pho-togrammetry and Remote Sensing, 60:284–294, 2006.

[18] J. F. Sturm. Using SeDuMi 1.02, a Matlab toolbox for opti-mization over symmetric cones. Optimization Methods andSoftware, 11-12:625–653, 1999.

[19] J. Tropp. Just relax: convex programming methods for iden-tifying sparse signals in noise. Information Theory, IEEETransactions on, 52(3):1030–1051, March 2006.

Figure 3. Two images from the dinosaur sequence, and the resulting reconstruction.

Figure 4. Two images from the house sequence, and the resulting reconstruction.

Figure 5. Two images from the church sequence, and the resulting reconstruction.

[15] Y. Seo, H. Lee, and S. W. Lee. Outlier removal by convexoptimization for l-infinity approaches. In PSIVT ’09: PacificRim Symposium on Advances in Image and Video Technol-ogy, 2009.

[16] K. Sim and R. Hartley. Removing outliers using the L1-norm. In Conf. Computer Vision and Pattern Recognition,pages 485–492, New York City, USA, 2006.

[17] H. Stewenius, C. Engels, and D. Nister. Recent develop-

ments on direct relative orientation. ISPRS Journal of Pho-togrammetry and Remote Sensing, 60:284–294, 2006.

[18] J. F. Sturm. Using SeDuMi 1.02, a Matlab toolbox for opti-mization over symmetric cones. Optimization Methods andSoftware, 11-12:625–653, 1999.

[19] J. Tropp. Just relax: convex programming methods for iden-tifying sparse signals in noise. Information Theory, IEEETransactions on, 52(3):1030–1051, March 2006.

Olsson  et  al.,  Efficient  op5miza5on  for  L-­‐inQy  problems  using  pseudoconvexity,  ICCV  2007.  Hartley  and  Kahl,  Op5mal  algorithms  in  mul5view  geometry,  ACCV  2007.  

5  of  45  

Example  3:  Homography  fiMng  

by  T.-­‐J.  Chin   Figure  from  hYp://sse.tongji.edu.cn/linzhang/CV14/Projects/panorama.htm.  

6  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Running  example:  Linear  regression  

by  T.-­‐J.  Chin  

ri(✓) = |bi � ✓ai|

xi = [ai, bi]T

b(a) = ✓a

✏

7  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

RANSAC,  minimal  subset  size  =  p  

by  T.-­‐J.  Chin  

8  of  45  

Minmax  problem  •  Minimise  the  maximum  residual:  

•  Same  as  L-­‐infinity  minimisa5on1,2:  

•  A.k.a.  Chebyshev  approxima5on/regression.  

by  T.-­‐J.  Chin  

min

✓max

i|bi � ✓ai|

min✓

���������

2

6664

|b1 � ✓a1||b2 � ✓a2|

...|bN � ✓aN |

3

7775

���������1

1Hartley  and  Schaffalitzky,  L-­‐inQy  minimiza5on  in  geometric  reconstruc5on  problems,  CVPR  2004.  2Kahl  and  Hartley,  Mul5ple-­‐view  geometry  under  the  L-­‐inQy-­‐norm,  PAMI  2008.  

9  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Minmax  problem  

by  T.-­‐J.  Chin  

10  of  45  

−1 −0.5 0 0.5 1 1.5 2 2.50

0.5

1

1.5

Minmax  problem  

by  T.-­‐J.  Chin  

|bi � ✓ai|

✓

11  of  45  

−1 −0.5 0 0.5 1 1.5 2 2.50

0.5

1

1.5

Minmax  problem  

by  T.-­‐J.  Chin  

max

i|bi � ✓ai|

Global  minimum  

✓✓⇤

12  of  45  

−1 −0.5 0 0.5 1 1.5 2 2.50

0.5

1

1.5

Simplex  algorithm  

by  T.-­‐J.  Chin  

✓

min✓

�

s.t. |bi � ✓ai| �

✓init

13  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Combinatorial  dimension  =  p+1  

by  T.-­‐J.  Chin  

Ac5ve  set  or  “basis”  

14  of  45  

−1 −0.5 0 0.5 1 1.5 2 2.50

0.5

1

1.5

Combinatorial  dimension  =  p+1  

by  T.-­‐J.  Chin  

✓✓⇤

Ac5ve  set  or  “basis”  

15  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Maximum  consensus  

by  T.-­‐J.  Chin  

I⇤

16  of  45  

0.25 0.3 0.35 0.4 0.450.2

0.25

0.3

0.35

0.4

Maximum  consensus  

by  T.-­‐J.  Chin  

I⇤min

✓max

i2I⇤|bi � ✓ai|

� ✏

17  of  45  

An  algorithm  

•  For  all  subsets                          of  size  (p+1);  •  Solve  minmax  problem  on          .  •  If  maximum  residual  of            is              ;  • If  the  coverage  of            is  greater  than  the  current  largest;  •   Set            as  the  coverage  of        .                                                  

 by  T.-­‐J.  Chin  

✏

BB

B

B

B ⇢ X

I⇤

✓N

p+ 1

◆=

N !

(p+ 1)!(N � p� 1)!

=1

(p+ 1)!N(N � 1) . . . (N � p) ⌘ O(Np+1)

18  of  45  

−1 −0.5 0 0.5 1 1.5 2 2.50

0.5

1

1.5

Minmax  problem  

by  T.-­‐J.  Chin  

19  of  45  

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

Minmax  problem  

by  T.-­‐J.  Chin  

20  of  45  

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

Recursive  minmax  

by  T.-­‐J.  Chin  

21  of  45  

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

Recursive  minmax  

by  T.-­‐J.  Chin  

22  of  45  

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

Recursive  minmax  

by  T.-­‐J.  Chin  

23  of  45  

0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

Recursive  minmax  

by  T.-­‐J.  Chin  

24  of  45  

It’s  a  tree!  

by  T.-­‐J.  Chin  

Level 0

Level 1

Level 2

Level 3Level 4

Adjacent bases

f(B)

θ(B)

25  of  45  

Tree  depth  or  level  

by  T.-­‐J.  Chin  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Level 0

Level 1

Level 2

Level 3Level 4

Level-0 basisf(B)

θ(B)

26  of  45  

Tree  depth  or  level  

by  T.-­‐J.  Chin  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Level 0

Level 1

Level 2

Level 3Level 4

Level-3 basis

f(B)

θ(B)

27  of  45  

Maximum  consensus  II  

by  T.-­‐J.  Chin  

minB

l(B) s.t. f(B) ✏.

Level 0

Level 1

Level 2

Level 3Level 4

f(B)

θ(B)

ε

Feasible

28  of  45  

Breadth-­‐first  search  (BFS)  

by  T.-­‐J.  Chin  

Level 0

Level 1

Level 2

Level 3Level 4

f(B)

θ(B)

ε

Feasible

29  of  45  

A*  algorithm  

•  Basis  expansion  is  priori5sed  by  

by  T.-­‐J.  Chin  

:  Level  of  basis          .    :  An  es5mate  of  the  number  of  steps  remaining  to  feasibility.  

e(B) = l(B) + h(B)

l(B)

h(B)

B

Hart  et  al.,  A  formal  basis  for  the  heuris5c  determina5on  of  minimum  cost  paths,  IEEE  Trans.  on  Systems  Science  and  Cyberne5cs,  4(2):100–107,  1968.  

30  of  45  

A*  algorithm  

by  T.-­‐J.  Chin  

A  basis  Bl(B)

h(B)

Level 0

Level 1

Level 2

Level 3Level 4

f(B)

θ(B)

ε

Feasible

31  of  45  

A*  algorithm  

by  T.-­‐J.  Chin  

Level 0

Level 1

Level 2

Level 3Level 4

f(B)

θ(B)

ε

Feasible

32  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Heuris5c  func5on  

by  T.-­‐J.  Chin  

O = {B1}

33  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Heuris5c  func5on  

by  T.-­‐J.  Chin  

O = {B1,B2}

34  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Heuris5c  func5on  

by  T.-­‐J.  Chin  

O = {B1,B2,B3}

35  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Heuris5c  func5on  

by  T.-­‐J.  Chin  

O = {B1,B2,B3,B4}

36  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Heuris5c  func5on  

by  T.-­‐J.  Chin  

O = {B1,B2,B3,B4,B5}

37  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Heuris5c  func5on  

by  T.-­‐J.  Chin  

h(B) = |{B1,B2,B3,B4,B5}| = 5

38  of  45  by  T.-­‐J.  Chin  

Defini&on  (Admissibility):  A  heuris5c  is  admissible  if  it  sa5sfies    where                        is  the  true  remaining  cost  from            to  feasibility.  

h(B) � 0 and h(B) h⇤(B)

h⇤(B) B

Theorem:  A*  algorithm  is  op5mal  if                    is  admissible.  h(B)

39  of  45  

Results  

by  T.-­‐J.  Chin  

0 0.2 0.4 0.6 0.8 1 1.2−0.6

−0.4

−0.2

0

0.2

0.4

A* result (global) vs RANSAC result

2D PointsRANSAC fitA* fitRANSAC inliersCommon inliersA* inliers

40  of  45  

Results  

by  T.-­‐J.  Chin  

0 5 10 15 20 250

5

10

15

20

Number of outliers

Run

time

(s)

RANSACMaxFSMatousekBFSA*

41  of  45  

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Limita5on:  Outlier  ra5o  

by  T.-­‐J.  Chin  

h(B) = |{B1,B2,B3,B4,B5}| = 5

1

p+ 1

42  of  45  

Figure 3. Two images from the dinosaur sequence, and the resulting reconstruction.

Figure 4. Two images from the house sequence, and the resulting reconstruction.

Figure 5. Two images from the church sequence, and the resulting reconstruction.

[15] Y. Seo, H. Lee, and S. W. Lee. Outlier removal by convexoptimization for l-infinity approaches. In PSIVT ’09: PacificRim Symposium on Advances in Image and Video Technol-ogy, 2009.

[16] K. Sim and R. Hartley. Removing outliers using the L1-norm. In Conf. Computer Vision and Pattern Recognition,pages 485–492, New York City, USA, 2006.

[17] H. Stewenius, C. Engels, and D. Nister. Recent develop-

ments on direct relative orientation. ISPRS Journal of Pho-togrammetry and Remote Sensing, 60:284–294, 2006.

[18] J. F. Sturm. Using SeDuMi 1.02, a Matlab toolbox for opti-mization over symmetric cones. Optimization Methods andSoftware, 11-12:625–653, 1999.

[19] J. Tropp. Just relax: convex programming methods for iden-tifying sparse signals in noise. Information Theory, IEEETransactions on, 52(3):1030–1051, March 2006.

Other  residual  func5ons?  

Triangula&on  

 Reprojec5on  error:  

Homography  fi<ng  

Transfer  error:  

by  T.-­‐J.  Chin  

ri(✓) =k(Pi,1:2 � xiPi,3)✓k

Pi,3✓ri(✓) =

k(✓1:2 � u0i✓3)uik

✓3ui

43  of  45  

Pseudoconvex  residual  

by  T.-­‐J.  Chin  

α

✓init ✓⇤

44  of  45  

Combinatorial  dimension  =  p+1  

by  T.-­‐J.  Chin  

45  of  45  

Thank  you!  

by  T.-­‐J.  Chin  

JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 14

shape matching and similarity,” ACM TOG, vol. 25, pp. 130–150,2006.

[21] B. Jian and B. Vemuri, “A robust algorithm for point set registra-tion using mixture of Gaussians,” in ICCV, 2005.

[22] A. Mynorenko and X. Song, “Point set registration: coherent pointdrift,” IEEE TPAMI, vol. 32, no. 1, pp. 2262–2275, 2010.

[23] A. Makadia, A. Patterson, and K. Daniilidis, “Fully automaticregistration of 3D point clouds,” in CVPR, 2006.

[24] N. Gelfand, N. Mitra, L. Guibas, and H. Pottmann, “Robust globalregistration,” in Eurographics, 2005.

[25] C. Olsson, O. Enqvist, and F. Kahl, “A polynomial-time boundfor natching and registration with outliers,” in CVPR, 2008.

[26] E. Ask, O. Enqvist, and F. Kahl, “Optimal geometric fitting underthe truncated l2-norm,” in CVPR, 2013.

[27] H. Li and R. Hartley, “The 3D–3D registration problem revisited,”in ICCV, 2007.

[28] O. Enqvist, K. Josephson, and F. Kahl, “Optimal correspondencesfrom pairwise constraints,” in ICCV, 2009.

[29] M. Leordeanu and M. Hebert, “A spectral technique for corre-spondence problems using pairwise constraints,” in ICCV, 2007.

[30] C. Olsson, F. Kahl, and M. Oskarsson, “Branch-and-bound meth-ods for Euclidean registration problems,” IEEE TPAMI, vol. 31,no. 5, pp. 783–794, 2009.

[31] J.-C. Bazin, H. Li, I. S. Kweon, C. Demonceaux, P. Vasseur, andK. Ikeuchi, “A branch and bound approach to correspondenceand grouping problem,” IEEE TPAMI, 2013.

[32] J. O’Rourke, Computational geometry in C. Cambridge UniversityPress, 1998.

[33] S. Rusinkiewicz and M. Levoy, “Efficient variants of the ICPalgorithm,” in Int’l Conf. on 3-D Digital Imaging and Modeling(3DIM), 2001.

[34] B. Curless and M. Levoy, “A volumetric method for buildingcomplex models from range images,” SIGGRAPH, 1996.

Alvaro Parra Bustos received a BSc Eng.(2006), a Computer Science Engineer degree(2008) and a M.Sc. degree in Computer Sci-ence (2011) from Universidad de Chile (Santi-ago, Chile). He is currently a PhD student withinthe Australian Centre for Visual Technologies(ACVT) in the University of Adelaide, Australia.His main research interests include point cloudregistration, 3D computer vision and optimisa-tion methods in computer vision.

Tat-Jun Chin received a B.Eng. in MechatronicsEngineering from Universiti Teknologi Malaysia

in 2003 and subsequently in 2007 a PhD in Com-puter Systems Engineering from Monash Uni-versity, Victoria, Australia. He was a ResearchFellow at the Institute for Infocomm Researchin Singapore 2007- 2008. Since 2008 he is aLecturer at The University of Adelaide, Australia.His research interests include robust estimation,computational geometry, and statistical learningmethods in Computer Vision.

Anders Eriksson received the M.Sc. degree inelectrical engineering and the PhD degree inmathematics from Lund University, Sweden, in2000 and 2008, respectively. Currently, he is asenior research associate at the University ofAdelaide, Australia. His research interests in-clude optimization theory and numerical meth-ods applied to the fields of computer vision andmachine learning.

Hongdong Li received the M.Sc. and PhD de-grees in information and electronics engineer-ing in 1996 and 2000, respectively, both fromZhejiang University, China. Since 2004 he hasjoined the Australian National University (ANU)as a research fellow and is also seconded to Na-tional ICT Australia (NICTA) Canberra Labs. Heis currently a faculty member with the ResearchSchool of Engineering, ANU. He is the recipientof the CVPR’12 Best Paper Award. His currentresearch interests include geometric computer

vision, pattern recognition, computer graphics, and combinatorial opti-mization.

David Suter received a B.Sc. degree inapplied mathematics and physics (TheFlinders University of South Australia 1977), aGrad. Dip. Comp. (Royal Melbourne Instituteof Technology 1984)), and a Ph.D. in computerscience (La Trobe University, 1991). He was aLecturer at La Trobe from 1988 to 1991; anda Senior Lecturer (1992), Associate Professor(2001), and Professor (2006-2008) at MonashUniversity, Melbourne, Australia. Since 2008 hehas been a professor in the school of Computer

Science, The University of Adelaide. He is head of the School ofComputer Science. He served on the Australian Research Council(ARC) College of Experts from 2008-2010. He is on the editorial boardof International Journal of Computer Vision. He has previously servedon the editorial boards of Machine Vision and Applications and theInternational Journal of Image and Graphics. He was General co-Chairor the Asian Conference on Computer Vision (Melbourne 2002) andis currently co-Chair of the IEEE International Conference on ImageProcessing (ICIP2013).

JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007 14

shape matching and similarity,” ACM TOG, vol. 25, pp. 130–150,2006.

[21] B. Jian and B. Vemuri, “A robust algorithm for point set registra-tion using mixture of Gaussians,” in ICCV, 2005.

[22] A. Mynorenko and X. Song, “Point set registration: coherent pointdrift,” IEEE TPAMI, vol. 32, no. 1, pp. 2262–2275, 2010.

[23] A. Makadia, A. Patterson, and K. Daniilidis, “Fully automaticregistration of 3D point clouds,” in CVPR, 2006.

[24] N. Gelfand, N. Mitra, L. Guibas, and H. Pottmann, “Robust globalregistration,” in Eurographics, 2005.

[25] C. Olsson, O. Enqvist, and F. Kahl, “A polynomial-time boundfor natching and registration with outliers,” in CVPR, 2008.

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Alvaro Parra Bustos received a BSc Eng.(2006), a Computer Science Engineer degree(2008) and a M.Sc. degree in Computer Sci-ence (2011) from Universidad de Chile (Santi-ago, Chile). He is currently a PhD student withinthe Australian Centre for Visual Technologies(ACVT) in the University of Adelaide, Australia.His main research interests include point cloudregistration, 3D computer vision and optimisa-tion methods in computer vision.

Tat-Jun Chin received a B.Eng. in MechatronicsEngineering from Universiti Teknologi Malaysia

in 2003 and subsequently in 2007 a PhD in Com-puter Systems Engineering from Monash Uni-versity, Victoria, Australia. He was a ResearchFellow at the Institute for Infocomm Researchin Singapore 2007- 2008. Since 2008 he is aLecturer at The University of Adelaide, Australia.His research interests include robust estimation,computational geometry, and statistical learningmethods in Computer Vision.

Anders Eriksson received the M.Sc. degree inelectrical engineering and the PhD degree inmathematics from Lund University, Sweden, in2000 and 2008, respectively. Currently, he is asenior research associate at the University ofAdelaide, Australia. His research interests in-clude optimization theory and numerical meth-ods applied to the fields of computer vision andmachine learning.

Hongdong Li received the M.Sc. and PhD de-grees in information and electronics engineer-ing in 1996 and 2000, respectively, both fromZhejiang University, China. Since 2004 he hasjoined the Australian National University (ANU)as a research fellow and is also seconded to Na-tional ICT Australia (NICTA) Canberra Labs. Heis currently a faculty member with the ResearchSchool of Engineering, ANU. He is the recipientof the CVPR’12 Best Paper Award. His currentresearch interests include geometric computer

vision, pattern recognition, computer graphics, and combinatorial opti-mization.

David Suter received a B.Sc. degree inapplied mathematics and physics (TheFlinders University of South Australia 1977), aGrad. Dip. Comp. (Royal Melbourne Instituteof Technology 1984)), and a Ph.D. in computerscience (La Trobe University, 1991). He was aLecturer at La Trobe from 1988 to 1991; anda Senior Lecturer (1992), Associate Professor(2001), and Professor (2006-2008) at MonashUniversity, Melbourne, Australia. Since 2008 hehas been a professor in the school of Computer

Science, The University of Adelaide. He is head of the School ofComputer Science. He served on the Australian Research Council(ARC) College of Experts from 2008-2010. He is on the editorial boardof International Journal of Computer Vision. He has previously servedon the editorial boards of Machine Vision and Applications and theInternational Journal of Image and Graphics. He was General co-Chairor the Asian Conference on Computer Vision (Melbourne 2002) andis currently co-Chair of the IEEE International Conference on ImageProcessing (ICIP2013).

Pulak  Purkait  Adelaide  

Anders  Eriksson  QUT  

David  Suter  Adelaide  

Tat-­‐Jun  Chin  Adelaide