title: Integral invariants for shape matching.
abstract: For shapes represented as closed planar contours, we introduce a class of functionals which are invariant with respect to the Euclidean group and which are obtained by performing integral operations. While such integral invariants enjoy some of the desirable properties of their differential counterparts, such as locality of computation (which allows matching under occlusions) and uniqueness of representation (asymptotically), they do not exhibit the noise sensitivity associated with differential quantities and, therefore, do not require presmoothing of the input shape. Our formulation allows the analysis of shapes at multiple scales. Based on integral invariants, we define a notion of distance between shapes. The proposed distance measure can be computed efficiently and allows warping the shape boundaries onto each other; its computation results in optimal point correspondence as an intermediate step. Numerical results on shape matching demonstrate that this framework can match shapes despite the deformation of subparts, missing parts and noise. As a quantitative analysis, we report matching scores for shape retrieval from a database.
authors.affiliation: Electronics Engineering Technologies Division, Lawrence Livermore National Laboratory, PO Box 508, L-290 Livermore, CA 94551-0508, USA. smanay.ece98@gtalumni.org
authors.forename: Siddharth
authors.initials: S
authors.lastname: Manay
authors.forename: Daniel
authors.initials: D
authors.lastname: Cremers
authors.forename: Byung-Woo
authors.initials: BW
authors.lastname: Hong
authors.forename: Anthony J
authors.initials: AJ
authors.lastname: Yezzi
authors.forename: Stefano
authors.initials: S
authors.lastname: Soatto
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013382:Subtraction Technique