Bibliography

1

`Circle bundles over a complex quadric', J. London Math. Soc. 43 (1968), 323-324.

2

`Topology of double points of rank zero on three-folds in C^4 ' , J. London Math. Soc. 44 (1969), 523-530.

3

`What is an asymptote?', Math. Gazette 26 (1972), 274-284. Translated as `¿Que es una asymtota?', Boletin de Math. (Bogota) 9 (1975), 171-188.

4

`On the singularities of two related hypersurfaces', J. London Math. Soc. 7 (1973), 367-375.

5

P.J.Giblin and J.E. Reeve `Herszberg's singularities', Proc. London Math. Soc. (3) 28 (1974), 547-576.

6

J.W.Bruce and P.J.Giblin `On real simple singularities', Math. Proc. Camb. Philos. Soc. 88 (1980), 273-279.

7

J.W.Bruce and P.J.Giblin `A stratification of the space of plane quartic curves', Proc. London Math. Soc. (3) 42 (1981), 270-298.

8

J.W.Bruce, P.J.Giblin and C.G.Gibson `On caustics of plane curves', Amer. Math. Monthly 88 (1981), 651-667.

9

J.W.Bruce and P.J.Giblin `Generic curves and surfaces', J. London Math. Soc. 24 (1981), 555-561.

10

P.J.Giblin and C.G.Gibson `On regularity conditions over exceptional unimodular families of singularities', Quart. J. Math. (Oxford) (2) 32 (1981), 23-43.

11

J.W.Bruce and P.J.Giblin `What is an envelope?', Math. Gazette 65 (1981), 186-192.

12

P.J.Giblin and C.M.Hui `Specializations of complex quartic curves', Math. Proc. Camb. Philos. Soc. 91 (1982), 171-181.

13

P.J.Giblin and M.G. Soares `Recognizing singularities of surfaces in C^3 ', Math. Proc. Camb. Philos. Soc. 91 (1982), 17-27.

14

J.W.Bruce, P.J.Giblin and C.G.Gibson `On caustics by reflexion', Topology 21 (1982), 179-199.

15

J.W.Bruce, P.J.Giblin and C.G.Gibson `Source genericity of caustics by reflexion in the plane', Quart. J. Math. (Oxford) 33 (1982), 169-190.

16

J.W.Bruce, P.J.Giblin and C.G.Gibson `Source genericity of caustics by reflexion in ', Philos. Trans. Royal Soc. London 381 (1982), 83-116.

17

J.W.Bruce and P.J.Giblin `Generic curves and surfaces, II', J. London Math Soc. 26 (1982), 174-182.

18

`Parallels', Math. Gazette 66 (1982), 28-30.

19

Three problems on caustics, Amer. Math. Monthly 89 (1982), 594 and 90 (1983), 121; Mathematics Magazine Sept. 1982.

20

J.W.Bruce, P.J.Giblin and C.G.Gibson `Caustics by reflexion in the extended plane', Geometriae Dedicata 15 (1983), 171-194.

21

J.W.Bruce, P.J.Giblin and C.G.Gibson `Genericity of caustics by reflexion', Proc. Symposia in Pure Math, A.M.S., 40 (1983), 179-193.

22

J.W.Bruce and P.J.Giblin `Generic geometry', Amer. Math., Monthly 90 (1983), 529-545.

23

J.W.Bruce, P.J.Giblin and C.G.Gibson `Caustics by reflexion in extended space', Society for Industrial and Applied Mathematics Journal of Math. Analysis 15 (1984), 50-68.

24

J.W.Bruce, P.J.Giblin and C.G.Gibson `Caustics through the looking glass', Math. Intelligencer 6 (1984), 47-58.

25

J.W.Bruce and P.J.Giblin `One-parameter families of caustics by reflexion in the plane', Quart. J. Math (Oxford) 35 (1984), 243-251.

26

D.L.Fidal and P.J.Giblin `Generic one-parameter families of caustics in the plane', Math. Proc. Camb. Philos. Soc. 96 (1984), 425-432.

27

J.W.Bruce and P.J.Giblin `An elementary approach to generic properties of plane curves', Proc. Amer. Math. Soc. 90 (1984), 455-458.

28

J.W.Bruce and P.J.Giblin `Smooth maps of discriminant varieties', Proc. London. Math. Soc. 50 (1985), 535-551.

29

J.W.Bruce and P.J.Giblin `Outlines and their duals', Proc. London Math. Soc. 50 (1985), 552-570.

30

J.W.Bruce and P.J.Giblin `Two-parameter families of caustics by reflexion', Proc. London Math. Soc. 50 (1985), 571-576.

31

J.W.Bruce , P.J.Giblin and C.G.Gibson `Symmetry sets', Proc. Royal Soc. Edinburgh 101A (1985), 163-186.

32

P.J.Giblin and S.A.Brassett `Local symmetry of plane curves', Amer. Math. Monthly 92 (1985), 689-707.

33

`Computer graphics in geometry courses', Internat. J. of Math. Education in Science and Technology 16 (1985), 365-371.

34

J.W.Bruce and P.J.Giblin `Growth, motion and one-parameter families of symmetry sets', Proc. Royal Soc. Edinburgh 104A (1986), 179-204.

35

P.J.Giblin and J. Kingston `Stable triple crossings on caustics by reflexion in the plane' Quarterly J. Math. (Oxford) 37 (1986). 17-25.

36

P.J.Giblin, I.R.Porteous, A. Veevers and G.Walker `Challenge on Merseyside', Math. Intelligencer 8 (1986), 57-63.

37

J.W.Bruce and P.J.Giblin `Generic isotopies of space curves', Glasgow Math. J. 29 (1987), 41-63.

38

T.F.Banchoff and P.J.Giblin `Global theorems for symmetry sets of smooth curves and polygons in the plane', Proc. Royal Soc. Edinburgh 106A (1987), 221-231.

39

P.J.Giblin and R.Weiss `Reconstruction of surfaces from profiles', Proc. First Internat. Conf. on Computer Vision, London, 1987; Computer Society of the IEEE, pp. 136-144. HERE

40

P.J.Giblin and M.G.Soares `On the geometry of a surface and its singular profiles', Image and Vision Computing 6 (1988), 225-234.

41

J.W.Bruce and P.J.Giblin `Families of spheres and circles', Banach Center Publications, Warsaw, Vol. 20 (Singularities) (1988), 85-102.

42

A.Zisserman, P.J.Giblin and A. Blake `The information available to a moving observer from specularities', Image and Vision Computing 7 (1989), 38-42.

43

P.J.Giblin and D.O'Shea `The bitangent sphere problem', Amer. Math. Monthly 97 (1990), 5-23.

44

J.W.Bruce and P.J.Giblin `Projections of surfaces with boundary', Proc. London Math. Soc. (3) 60 (1990), 392-416

45

P.J.Giblin and F.Tari `Local reflexional and rotational symmetry in the Plane', Singularity Theory and its Applications, Springer Lecture Notes in Math. 1462 (1991) 154-171.

46

F.E.Pollick, P.J.Giblin, J.Rycroft and L.L.Wilson, `Human recovery of shape from profiles', Behaviormetrika 19 (1992), 65-79.

47

T.F.Banchoff and P.J.Giblin `Symmetry sets of piecewise circular curves', Proc. Royal Soc. Edinburgh 123A (1993), 1135-1149.

48

P.J.Giblin, J.E.Rycroft and F.E.Pollick, `Moving Surfaces', in Design and Applications of Curves and Surfaces: Mathematics of Surfaces V, Oxford University Press (IMA Conference Proceedings Series), 1994, pp. 433-453.

49

T.F.Banchoff and P.J.Giblin `On the geometry of piecewise- circular curves', Amer. Math. Monthly 101 (1994), 403-416.

50

P.J.Giblin, F.E.Pollick and J.E.Rycroft, `Recovery of an unknown axis of rotation from the profiles of a rotating surface', J.Optical Soc. America 11A (1994), 1976-1984.

51

P.J.G and R.S.Weiss, `Epipolar fields on surfaces', Computer Vision - ECCV 94, Ed. J.-0. Eklundh, Springer Lecture Notes in Computer Science 800 (1994), 14-23

52

M.W.Wright, R.Cipolla and P.J.Giblin, `Skeletonisation using an extended Euclidean distance transform', Proc. British Machine Vision Conference (Ed. E. Hancock), Vol II, 1994, pp.559-568; also Image and Vision Computing 13 (1995), 367-375.

53

P.J.Giblin and R.S.Weiss, `Epipolar curves on surfaces', Image and Vision Computing 13 (1995), 33-44.HERE

54

P.J.Giblin and F.Tari, `Perpendicular bisectors, duals and local symmetry', Proc. Royal Soc. Edinburgh 125A (1995), 181-194.

55

J.W.Bruce, P.J.Giblin and F.Tari, `Families of surfaces: height functions, Gauss maps and duals', in Real and Complex Singularities, W.L.Marar(ed.), Pitman Research Notes in Mathematics, Vol. 333 (1995), 148-178.

56

R.Cipolla, G.Fletcher and P.J.Giblin, `Surface geometry from cusps of apparent contours', Proc. Int. Conf. on Computer Vision June 1995 (IEEE Computer Society Press), pp. 858-863.

57

R.Cipolla, K.Åström and P.J.Giblin `Motion from the frontier of curved surfaces', Proc. Int. Conf. on Computer Vision June 1995 (IEEE Computer Society Press), pp. 269-275.

58

M.W.Wright, A.Fitzgibbon, P.J.Giblin and R.B.Fisher, `Convex hulls, occluding contours, aspect graphs and the Hough transform', Proc. British Machine Vision Conference 1995, p. 493-502, and Image and Vision Computing 14 (1996), 627-634.

59

R.Cipolla, G.Fletcher and P.J.Giblin, `Following cusps', Int. J. Computer Vision 23 (1997), 115-129.

60

J.W.Bruce, P.J.Giblin and F.Tari, `Parabolic curves of evolving surfaces,' Int. J. Computer Vision. 17 (1996), 291-306.

61

J.W.Bruce, P.J.Giblin and F.Tari, `Ridges, crests and sub-parabolic lines of evolving surfaces', Int. J. Computer Vision. 18 (1996), 195-210.

62

G.Fletcher and P.J.Giblin, `Class based reconstruction techniques using singular apparent contours', Proc. European Conference on Computer Vision 1996, Lecture Notes in Computer Science 1064, Springer-Verlag, 107-116.

63

K.Åström, R.Cipolla and P.J.Giblin, `Generalised epipolar constraints', Proc. European Conference on Computer Vision 1996, Lecture Notes in Computer Science 1065, Springer-Verlag, 97-108.

64

M.W.Wright, A.Fitzgibbon, P.J.Giblin and R.B.Fisher, `Beyond the Hough transform: further properties of the mapping and their applications', European Conf. on Computer Vision Workshop 1996, Springer Lecture Notes in Computer Science 1144, pp. 361-380.

65

P.J.Giblin and M.Trout, `Symmetric and almost symmetric polygons', Math. Gazette (1997), 381-390.

66

G.Fletcher and P.J.Giblin, `Apparent contours, surfaces and motion', Proceedings of International Workshop on Computer Vision and Applied Geometry, Sophus Lie Institute, Nordfjordeid, Norway, August 1995.

67

J.W.Bruce, P.J.Giblin and F.Tari, `Special surfaces and their duals', Proceedings of International Workshop on Computer Vision and Applied Geometry, Sophus Lie Institute, Nordfjordeid, Norway, August 1995.

68

J.W.Bruce, P.J.Giblin and F.Tari, `Families of surfaces: height functions and projections to planes', Math. Scand 82 (1998), 165-185.

69

P.J.Giblin and G.Sapiro, `Affine invariant distances, envelopes and symmetry sets', Technical Report HPL-96-93, Hewlett-Packard, June 1996; Geom. Dedicata 71 (1998), 237-261.

70

P.J.Giblin and G.Sapiro, `Affine invariant symmetry sets', in F.Cucker et al. (eds.), Foundations of Computational Mathematics, Selected papers of a conference at IMPA, Rio di Janeiro, Brazil, January 1997, Springer-Verlag, pp. 152-168.

71

P.J.Giblin and G.Sapiro, `Affine invariant medial axis and skew symmetry', Proceedings of International Conf. on Computer Vision, Bombay 1998, pp.833-838.

72

P.J.Giblin, `Apparent contours: an outline', Phil. Trans. Royal Soc. London 356 (1998), 1087-1102.

73

P.J.Giblin and M.Trout, `Cusps on wheels on wheels on wheels', Math. Magazine 71 (1998), 309-313.

74

J.W.Bruce, P.J.Giblin and F.Tari, `Families of surfaces: focal sets, ridges and umbilics', Math. Proc. Camb. Phil. Soc 125 (1999), 243-268.

75

K.Åström, R.Cipolla and P.J.Giblin, `Generalised epipolar Constraints,' Int. J. Computer Vision 33 (1999) 51-72.

76

P.J.Giblin and P.A.Holtom, `The centre symmetry set', Geometry and Topology of Caustics, Banach Center Publications, Vol 50, ed. S.Janeczko and V.M.Zakalyukin, Warsaw, 1999, pp.91-105.

77

P.J.Giblin and G.Sapiro, `Affine versions of the symmetry set', Real and Complex Singularities, ed. J.W.Bruce and F.Tari, Chapman and Hall/CRC Research Notes in Mathematics 412 (1999) 173-187.

78

P. J. Giblin and B. B. Kimia, `On the Intrinsic Reconstruction of Shape from its Symmetries', Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR99) IEEE Computer Society Press (1999), 79-84.

79

P. J. Giblin and B. B. Kimia, `On the Local Form and Transitions of Symmetry Sets, and Medial Axes, and Shocks in 2D', Proceedings of the Fifth International Conference on Computer Vision (ICCV99) IEEE Computer Society Press (1999), 385-391.

80

S.Betelu, A.Tannenbaum, G.Sapiro and P.J.Giblin, `On the computation of the affine skeletons of planar curves and the detection of affine symmetry' Pattern Recognition 34 (2001), 943--952 .

81

P.J.Giblin and B.Kimia, `A formal classification of 3D medial axis points and their local geometry', to appear in the Proceedings of CVPR (IEEE Computer Society Conference on Computer Vision and Pattern Recognition), 2000.

82

S.Betelu, A.Tannenbaum, G.Sapiro and P.J.Giblin, `Noise resistant affine skeletons of planar curves', Proceedings of European Conference on Computer Vision, Dublin 2000, Lecture Notes in Computer Science 1842 (2000), 742-752, Springer-Verlag.

83

P.J.Giblin, `Symmetry sets and medial axes in two and three dimensions', The Mathematics of Surfaces, Roberto Cipolla and Ralph Martin (eds.), Springer-Verlag 2000, pp. 306--321.

84

S.Betelu, A.Tannenbaum, G.Sapiro and P.J.Giblin, `On the computation of the affine skeletons of planar curves and the detection of affine symmetry', Pattern Recognition 34 (2001), 943--952.

85

P.J.Giblin, `Zigzags', Mathematics Magazine 74 (2001) 259--272.

86

P.J.Giblin and B.B.Kimia, `Transitions of the 3D medial axis under a one-parameter family of deformations', Proceedings of the European Conference on Computer Vision 2002, Lecture Notes in Computer Science 2351 (2002), 718--734.

87

P.J.Giblin and V.M.Zakalyukin, `Singularities of families of chords', Functional Analysis and its Applications 36 (2002), 220--224.

88

P.J.Giblin and B.B.Kimia, `On the local form and Transitions of Symmetry Sets, Medial Axes, and Shocks', Int. J. Computer Vision 54 (2003), 143--157.

89

P.J.Giblin and B.B.Kimia, `On the Intrinsic Reconstruction of Shape from its Symmetries', IEEE Trans. Pattern Analysis and Machine Intelligence, 25 (2003), 895--911.

90

P.J.Giblin and P.A.Holtom, `Affine distance symmetry sets' Math. Scandinavica 93 (2003),247-267.

91

P.J.Giblin and B.B.Kimia, `A formal classification of 3D medial axis points and their local geometry', Pattern Recognition and Machine Intelligence 26 (2004), 238-251.

92

M.Niethammer, S.Belelu, G.Sapiro, A.Tannenbaum, P.Giblin, `Area based medial axis of planar curves', Int. J. Computer Vision 60 (2004), 203-224.

93

P.J.Giblin and B.B.Kimia, `A formal classification of 3D medial axis points and their local geometry', IEEE Transactions on Pattern Analysis and Machine Intelligence 26 (2004), 238-251.

94

P.J.Giblin, Obituary of Arthur Geoffrey Walker, Bulletin of the London Mathematical Society, 36 (2004), 271-280.

95

Arjan Kuijper, Ole Fogh Olsen, Peter Giblin, Philip Bille and Mads Nielsen, `From a 2D shape to a string structure via the symmetry set', Proceedings of 8th European Conference on Computer Vision, Springer Lecture Notes in Computer Science 3022 (2004), 313-325.

96

Anthony Pollitt, Peter Giblin and Benjamin Kimia, `Consistency conditions on the medial axis', Proceedings of 8th European Conference on Computer Vision, Springer Lecture Notes in Computer Science 3022 (2004), 530-541.

97

Frederic F. Leymarie, Benjamin B. Kimia and Peter J. Giblin, `Towards Surface Regularization via Medial Axis Transitions', International Conference on Pattern Recognition 2004, Proceedings, Vol III, p.123-126.

98

Marc Niethammer, Santiago Betelu, Guillermo Sapiro, Allen Tannenbaum, Peter J. Giblin Area-Based Medial Axis of Planar Curves, Int. J. Computer Vision 60 (2004), 203-224.

99

P.J.Giblin and V.M.Zakalyukin, `Singularities of centre symmetry sets', Proceedings of the London Mathematical Society 90 (2005), 132--166.

100

A.Diatta and P.J.Giblin, `Geometry of isophote curves', Scale Space and PDE Methods in Computer Vision, Lecture Notes in Computer Science 3459 (2005), 50--61.

101

Andre Diatta, Peter Giblin, Brendan Guilfoyle, Wilhelm Klingenberg, `Level sets of functions and symmetry sets of surface sections', Mathematics of Surfaces XI, Lecture Notes in Computer Science 3604 (2005), 147-160.

102

Arjan Kuijper, Ole Fogh Olsen, Peter Giblin and Mads Neilsen, Alternative 2D shape representations using the symmetry set, Journal of Mathematical Imaging and Vision 26 (2006), 127-147.

103

Andre Diatta and Peter Giblin, Vertices and inflexions of plane sections of surfaces in R^3, Trends in Mathematics (Real and Complex Singularities), Birkhauser 2007, pp. 71-97.

104

P.J.Giblin and V.M.Zakalyukin, `Recognition of centre symmetry set singularities', Geometriae Dedicata 130 (2007), 43-58.

106

P.J.Giblin and B.B.Kimia, `Local Forms and Transitions of the Medial Axis', in Siddiqi, K., and Pizer, S., eds., Medial Representations: Mathematics, Algorithms and Applications. Springer, 2008.

107

Peter Giblin, `Affinely invariant symmetry sets', Caustics '06, Banach Center Publications 82 (2008), 71--84.

105

P.J.Giblin, B.B.Kimia and A.J.Pollitt, `Transitions of the 3D medial axis in a one-parameter family of surfaces',IEEE Transactions on Pattern Recognition and Machine Intelligence 31 (2009), 900-918.

108

F.Pollick , U.Maoz , A.Handzel , P.Giblin , G.Sapiro , T.Flash, `Three-dimensional arm movements at constant equi-affine speed', Cortex 45 (2009), 325--339.

109

James Damon, Peter Giblin and Gareth Haslinger, `Local image features resulting from 3-dimensional geometric features, illumination and movement: I', Int. J. Computer Vision 82 (2009), 25--47.

110

P.J.Giblin, J.P.Warder and V.M.Zakalyukin, `Bifurcations of affine equidistants', Proceedings of the Steklov Institute of Mathematics 267 (2009), 57--75.

111

James Damon, Peter Giblin and Gareth Haslinger, `Local image features resulting from 3-dimensional geometric features, illumination and movement: II', SIAM Journal of Imaging Sciences 4 (2011), 386-412.

112

P.J.Giblin and J.P.Warder, `Reconstruction from medial representations', American Mathematical Monthly 118 (2011), 712-725.

113

P.J.Giblin and S.Janeczko, `Geometry of surfaces via the contact map', Topology and its Applications 159 (2012), 466-475 (on-line http://dx.doi.org/10.1016/j.topol.2011.09.021).

114

P.J.Giblin and T.Sano, `Generic equi-centro-affine differential geometry of plane curves' Topology and its Applications 159 (2012), 476-483.

115

Ricardo Fabbri, Benjamin B. Kimia and Peter J.Giblin, `Camera Pose Estimation Using First-Order Curve Differential Geometry', in A. Fitzgibbon et al. (Eds.): ECCV 2012, Part IV, Lecture Notes in Computer Science Vol. 7575, pp. 229--242. Springer, Heidelberg (2012).

116

Peter Giblin, `Ancient approximation to the sine function', Math. Gazette. 98 (2014), 488--490.

117

P.J.Giblin and J.P.Warder, `Evolving Evolutoids', American Math. Monthly 121 (2014), 871--889.

118

P.J. Giblin and G.M.Reeve, `Centre symmetry sets of families of plane curves', Demonstratio Mathematica 48 (2015), 167--192

119

P.J.Giblin, `Applications of singularity theory and 3D modelling in arts and retail', pp. 265-271 in `UK Success Strories in Industrial Mathematics', ed. Philip Aston, Anthony Mulholland and Katherine Tant, Springer 2016.

120

P.J.Giblin and S.Janeczko, `Bifurcation sets of families of reflections on surfaces in R³', Proceedings of the Royal Society of Edinburgh 147A (2017), 337-352.

121

Peter Giblin and Graham Reeve, `Equidistants and their duals for families of plane curves', Advanced Studies in Pure Mathematics (Singularities in Generic Geometry) 78 (2018),251-272.

122

Azeb Alghanemi and Peter Giblin, `On the geometry of the midlocus associated to a smooth curve in the plane and space', Filomat 32 (2018), 2977-2990.

123

P.J.Giblin, S.Janeczko and M.A.S.Ruas, `Reflexion maps and geometry of surfaces in R⁴.' J. Singularities 21 (2020) 84-96.

124

Peter Giblin and Graham Reeve, `Equidistants for families of surfaces', J. Singularities 21 (2020), 97-118.

126

Peter Giblin and Stanislaw Janeczko, `Symmetrization of convex plane curves', Pure and Applied Mathematics Quarterly Journal 16 (2020), 1767-1787.

127

Ricardo Fabbri, Peter Giblin and Benjamin Kimia, `Camera pose estimation using first-order curve differential geometry', IEEE Transactions on Pattern Analysis and Machine Intelligence 43 (2021), 3321-3332.

128

Peter Giblin, Graham Reeve, Ricardo Uribe-Vargas, `Contact With Circles and Euclidean Invariants of Smooth Surfaces in R^3' The Quarterly Journal of Mathematics, 73 (2022), 937-967.

129

Peter Giblin, Graham Reeve, `Contact of circles with surfaces: answers to a question of Montaldi', Asian J. Math. 26 (2022), 613-615.

130

Peter Giblin and Aleksandr Pukhlikov, `Planar Sections of a Surface Close to an Umbilic', Arnold Mathematical Journal 9 (2023) 481-503.

131

Peter Giblin and Graham Reeve, `Bitangent planes and applications to thermodynamics', Journal of Geometry and Physics, 192 (2023).

132

Peter Giblin, `Four points, six distances', Math. Gazette 107 (2023), 517-523.

133

Bill Bruce, Peter Giblin, David Mond, Stephen Pizer and Les Wilson, `Jim Damon's contributions to singularity theory and its applications', in Handbook of Geometry and Topology of Singularities Vol VII, ed. Jose Luis Cisneros-Molina, Le Dung Trang, Jose Seade, 2024.