Noname manuscript No. (will be inserted by the editor) DaLI: Deformation and Light Invariant Descriptor

Abstract Recent advances in 3D shape analysis and recognition have shown that heat diffusion theory can be effectively used to describe local features of deform-ing and scaling surfaces. In this paper, we show how this description can be used to characterize 2D image patches, and introduce DaLI, a novel feature point de-scriptor with high resilience to non-rigid image trans-formations and illumination changes. In order to build the descriptor, 2D image patches are initially treated as 3D surfaces. Patches are then described in terms of a heat kernel signature, which captures both local and global information, and shows a high degree of invari-ance to non-linear image warps. In addition, by further applying a logarithmic sampling and a Fourier trans-form, invariance to photometric changes is achieved. Finally, the descriptor is compacted by mapping it onto a low dimensional subspace computed using Principal Component Analysis, allowing for an efficient matching. A thorough experimental validation demonstrates that DaLI is significantly more discriminative and robust to illuminations changes and image transformations than state of the art descriptors, even those specifically de-signed to describe non-rigid deformations. Keywords local image descriptors · diffusion equa-tion · heat kernel descriptors · deformation and illumination invarianc