2023
Bitangent planes of surfaces and applications to thermodynamics (Journal article)
Giblin, P., & Reeve, G. (2023). Bitangent planes of surfaces and applications to thermodynamics. JOURNAL OF GEOMETRY AND PHYSICS, 192. doi:10.1016/j.geomphys.2023.104920DOI: 10.1016/j.geomphys.2023.104920
Fabbri, R., Duff, T., Fan, H., Regan, M., de Pinho, D. D. C., Tsigaridas, E., . . . Pajdla, T. (2023). Trifocal Relative Pose From Lines at Points. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 45(6), 7870-7884. doi:10.1109/TPAMI.2022.3226165DOI: 10.1109/TPAMI.2022.3226165
2022
Giblin, P., Reeve, G., & Uribe-Vargas, R. (2022). Contact With Circles and Euclidean Invariants of Smooth Surfaces in Double-struck capital R-3. QUARTERLY JOURNAL OF MATHEMATICS, 73(3), 937-967. doi:10.1093/qmath/haab058DOI: 10.1093/qmath/haab058
CONTACT OF CIRCLES WITH SURFACES: ANSWERS TO A QUESTION OF MONTALDI (Journal article)
Giblin, P., & Reeve, G. (2022). CONTACT OF CIRCLES WITH SURFACES: ANSWERS TO A QUESTION OF MONTALDI. ASIAN JOURNAL OF MATHEMATICS, 26(5), 613-616. Retrieved from https://www.webofscience.com/
2020
Giblin, P., & Reeve, G. (2020). Equidistants for families of surfaces. Journal of Singularities, 21, 97-118. doi:10.5427/jsing.2020.21fDOI: 10.5427/jsing.2020.21f
Giblin, P. J., Janeczko, S., & Ruas, M. A. S. (2020). REFLEXION MAPS AND GEOMETRY OF SURFACES IN R-4. In JOURNAL OF SINGULARITIES Vol. 21 (pp. 84-96). doi:10.5427/jsing.2020.21eDOI: 10.5427/jsing.2020.21e
Fabbri, R., Duff, T., Fan, H., Regan, M. H., da Costa de Pinho, D., Tsigaridas, E., . . . Pajdla, T. (2020). TRPLP – Trifocal Relative Pose From Lines at Points. In 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). IEEE. doi:10.1109/cvpr42600.2020.01209DOI: 10.1109/cvpr42600.2020.01209
2017
Giblin, P. J., & Janeczko, S. (2017). Bifurcation sets of families of reflections on surfaces in R-3. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 147(2), 337-352. doi:10.1017/S0308210516000184DOI: 10.1017/S0308210516000184
2016
Single digits (Journal article)
Giblin, P. J. (2016). Single digits. MATHEMATICAL GAZETTE, 100(549), 548-549. doi:10.1017/mag.2016.135DOI: 10.1017/mag.2016.135
2015
CENTRE SYMMETRY SETS OF FAMILIES OF PLANE CURVES (Journal article)
Giblin, P., & Reeve, G. (2015). CENTRE SYMMETRY SETS OF FAMILIES OF PLANE CURVES. DEMONSTRATIO MATHEMATICA, 48(2), 167-192. doi:10.1515/dema-2015-0016DOI: 10.1515/dema-2015-0016
Centre symmetry sets of families of plane curves (Conference Paper)
Giblin, P. J., & Reeve, G. (2015). Centre symmetry sets of families of plane curves. In Demonstratio Mathematica Vol. 48 (pp. 167-192). doi:10.1515/dema-201-0016DOI: 10.1515/dema-201-0016
2014
Evolving Evolutoids (Journal article)
Giblin, P. J., & Warder, J. P. (2014). Evolving Evolutoids. AMERICAN MATHEMATICAL MONTHLY, 121(10), 871-889. doi:10.4169/amer.math.monthly.121.10.871DOI: 10.4169/amer.math.monthly.121.10.871
2007
Recognition of centre symmetry set singularities (Journal article)
Giblin, P. J., & Zakalyukin, V. M. (2007). Recognition of centre symmetry set singularities. Geometriae Dedicata, 130(1), 43-58. doi:10.1007/s10711-007-9204-2DOI: 10.1007/s10711-007-9204-2
Vertices and inflexions of plane sections of surfaces in ℝ3 (Chapter)
Giblin, P., & Diatta, A. (2007). Vertices and inflexions of plane sections of surfaces in ℝ3. In J. P. Brasselet, & M. A. S. Ruas (Eds.), Real and Complex Singularities (pp. 71-98). Basel - Boston - Berlin: Birkhauser. Retrieved from http://www.springer.com/
2006
Alternative 2D Shape Representations using the Symmetry Set (Journal article)
Kuijper, A., Olsen, O. F., Giblin, P., & Nielsen, M. (2006). Alternative 2D Shape Representations using the Symmetry Set. Journal of Mathematical Imaging and Vision, 26(1-2), 127-147. doi:10.1007/s10851-006-8372-2DOI: 10.1007/s10851-006-8372-2
'Vertices and inflexions of plane sections of surfaces in R^3' (Conference Paper)
Diatta, A., & Giblin, P. J. (2006). 'Vertices and inflexions of plane sections of surfaces in R^3'. In Real and Complex Singularities (pp. 71-97). Marseille: Birkhäuser, Basel, 2007. Retrieved from http://www.springerlink.com/content/vl34748x36773q05/
Matching 2D Shapes using the Symmetry Set (Conference Paper)
Kuijper, A., Olsen, O. F., Giblin, P. J., & Bille, P. (2006). Matching 2D Shapes using the Symmetry Set. In 18th International Conference on Pattern Recognition (ICPR 2006) Vol. II (pp. 179-182). Hong Kong: IEEE Computer Society, U.S..
2005
'Geometry of isophote curves' (Conference Paper)
Diatta, A., & Giblin, P. J. (2005). 'Geometry of isophote curves'. In 5th International Conference, Scale-Space 2005 Vol. 3459 (pp. 50-61). Hofgeismar, Germany: Springer Verlag. Retrieved from http://www.springerlink.com/content/tacmg6k362dbl6cc/
Geometry of isophote curves (Conference Paper)
Diatta, A., & Giblin, P. (2005). Geometry of isophote curves. In Scale Space and PDE Methods in Computer Vision Vol. 3459 (pp. 50-61). Hofgeismar, Germany: Springer-Verlag.
Level sets of functions and symmetry sets of surface sections (Conference Paper)
Diatta, A., Giblin, P., Guilfoyle, B., & Klingenberg, W. (2005). Level sets of functions and symmetry sets of surface sections. In Mathematics of Surfaces XI Vol. 3604 (pp. 49-60). Loughborough: Springer-Verlag.
Pre-symmetry Sets of 3D Shapes (Conference Paper)
Diatta, A., & Giblin, P. (2005). Pre-symmetry Sets of 3D Shapes. In Deep Structure, Singularities, and Computer Vision: First International Workshop Vol. 3753 (pp. 36-48). Maastricht: Springer-Verlag.
Singularities of centre symmetry sets (Journal article)
Giblin, P. J., & Zakalyukin, V. M. (2005). Singularities of centre symmetry sets. Proceedings of the London Mathematical Society, 90(01), 132-166. doi:10.1112/s0024611504014923DOI: 10.1112/s0024611504014923
2004
Area-Based Medial Axis of Planar Curves (Journal article)
Niethammer, M., Betelu, S., Sapiro, G., Tannenbaum, A., & Giblin, P. J. (2004). Area-Based Medial Axis of Planar Curves. International Journal of Computer Vision, 60(3), 203-224. doi:10.1023/b:visi.0000036835.28674.d0DOI: 10.1023/b:visi.0000036835.28674.d0
A formal classification of 3d medial axis points and their local geometry (Journal article)
Giblin, P., & Kimia, B. B. (2004). A formal classification of 3d medial axis points and their local geometry. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26(2), 238-251. doi:10.1109/tpami.2004.1262192DOI: 10.1109/tpami.2004.1262192
Consistency conditions on the medial axis (Conference Paper)
Giblin, P. J., Kimia, B. B., & Pollitt, A. J. (2004). Consistency conditions on the medial axis. In 8th European Conference on Computer Vision Vol. 3022 (pp. 530-541). Prague: Springer-Verlag.
From a 2D shape to a string structure via the symmetry set (Conference Paper)
Kuijper, A., Olsen, O. F., Giblin, P. J., Bille, P., & Nielsen, M. (2004). From a 2D shape to a string structure via the symmetry set. In 8th European Conference on Computer Vision Vol. 3022 (pp. 313-325). Prague: Springer-Verlag.
2003
On the intrinsic reconstruction of shape from its symmetries (Journal article)
Giblin, P. J., & Kimia, B. B. (2003). On the intrinsic reconstruction of shape from its symmetries. IEEE Transactions on Pattern Analysis and Machine Intelligence, 25(7), 895-911. doi:10.1109/tpami.2003.1206518DOI: 10.1109/tpami.2003.1206518
`Affine distance symmetry sets' (Journal article)
Giblin, P. J., & Holtom, P. A. (2003). `Affine distance symmetry sets'. Mathematica Scandinavica, 93(2), 247-267.
`On the local form and Transitions of Symmetry Sets, Medial Axes and Shocks' (Journal article)
Giblin, P. J., & Kimia, B. B. (2003). `On the local form and Transitions of Symmetry Sets, Medial Axes and Shocks'. International Journal of Computer Vision, 54(1-2), 143-157.
2002
`Transitions of the 3D medial axis under a one-parameter family of deformations' (Conference Paper)
Giblin, P. J., & Kimia, B. B. (2002). `Transitions of the 3D medial axis under a one-parameter family of deformations'. In A. Heyden, G. Sparr, M. Nielsen, & P. Johansen (Eds.), 7th European Conference on Computer Vision Vol. LNCS 2 (pp. 718-724). Copenhagen: Springer-verlag.
2001
On the computation of the affine skeletons of planar curves and the detection of skew symmetry (Journal article)
Betelu, S., Sapiro, G., Tannenbaum, A., & Giblin, P. J. (2001). On the computation of the affine skeletons of planar curves and the detection of skew symmetry. Pattern Recognition, 34(5), 943-952. doi:10.1016/s0031-3203(00)00045-5DOI: 10.1016/s0031-3203(00)00045-5
‘Mathematical explorations with MATLAB (Russian Translation) (Book)
Chen, K., Giblin, P. J., & Irving, A. C. (2001). ‘Mathematical explorations with MATLAB (Russian Translation). Moscow: Mir Publishers.
Zigzags (Journal article)
Giblin, P. J. (2001). Zigzags. Mathematics Magazine, 74, 259-272.
2000
Singularities of families of chords (Journal article)
Giblin, P. J., & Zakalyukin, V. M. (2000). Singularities of families of chords. Functional Analysis and Its Applications, 36(3), 220-224.
