Shape-from-shading using the heat equation
| dc.contributor.author | Robles-Kelly, Antonio | |
| dc.date.accessioned | 2015-12-08T22:08:44Z | |
| dc.date.issued | 2007 | |
| dc.date.updated | 2015-12-08T07:19:14Z | |
| dc.description.abstract | This paper offers two new directions to shape-from-shading, namely the use of the heat equation to smooth the field of surface normals and the recovery of surface height using a low-dimensional embedding. Turning our attention to the first of these contributions, we pose the problem of surface normal recovery as that of solving the steady state heat equation subject to the hard constraint that Lambert's law is satisfied. We perform our analysis on a plane perpendicular to the light source direction, where the z component of the surface normal is equal to the normalized image brightness. The x-y or azimuthal component of the surface normal is found by computing the gradient of a scalar field that evolves with time subject to the heat equation. We solve the heat equation for the scalar potential and, hence, recover the azimuthal component of the surface normal from the average image brightness, making use of a simple finite difference method. The second contribution is to pose the problem of recovering the surface height function as that of embedding the field of surface normals on a manifold so as to preserve the pattern of surface height differences and the lattice footprint of the surface normals. We experiment with the resulting method on a variety of real-world image data, where it produces qualitatively good reconstructed surfaces. | |
| dc.identifier.issn | 1057-7149 | |
| dc.identifier.uri | http://hdl.handle.net/1885/28720 | |
| dc.publisher | Institute of Electrical and Electronics Engineers (IEEE Inc) | |
| dc.source | IEEE Transactions on Image Processing | |
| dc.subject | Keywords: Finite difference method; Light sources; Luminance; Surface reconstruction; Heat equation; Lambert's law; Shape-from-shading; Surface normal recovery; Image reconstruction; algorithm; article; automated pattern recognition; computer assisted diagnosis; ev | |
| dc.title | Shape-from-shading using the heat equation | |
| dc.type | Journal article | |
| local.bibliographicCitation.issue | 1 | |
| local.bibliographicCitation.lastpage | 21 | |
| local.bibliographicCitation.startpage | 7 | |
| local.contributor.affiliation | Robles-Kelly, Antonio, College of Engineering and Computer Science, ANU | |
| local.contributor.authoremail | u1811090@anu.edu.au | |
| local.contributor.authoruid | Robles-Kelly, Antonio, u1811090 | |
| local.description.embargo | 2037-12-31 | |
| local.description.notes | Imported from ARIES | |
| local.identifier.absfor | 080104 - Computer Vision | |
| local.identifier.ariespublication | u3594520xPUB60 | |
| local.identifier.citationvolume | 16 | |
| local.identifier.doi | 10.1109/TIP.2006.884945 | |
| local.identifier.scopusID | 2-s2.0-33847717113 | |
| local.identifier.uidSubmittedBy | u3594520 | |
| local.type.status | Published Version |
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