Feature Detection Using Curvature Maps and the Min-Cut/Max-Flow Graph Cut Algorithm

Automatic detection of features in three-dimensional objects is a critical part of shape matching tasks such as object registration and recognition. Previous approaches to local surface matching have either focused on man-made objects, where features are generally well-defined, or required some type of user interaction to select features. Manual selection of corresponding features and subjective determination of the difference between objects are time consuming processes requiring a high level of expertise. Curvature is a useful property of a surface, but curvature calculation on a discrete mesh is often noisy and not always accurate. However, the {\em Curvature Map}, which represents shape information for a point and its surrounding region, is robust with respect to grid resolution and mesh regularity. It can be used as a measure of local surface similarity. We use these curvature map properties to extract features and segment the surface accordingly. Although thresholding techniques can be used to generate reasonable features, the choice of a threshold is very subjective and the results may be very sensitive to this choice. To avoid the threshold dilemma and to make the selection of the feature region less subjective, we employ a min-cut/max-flow graph cut algorithm, with vertex weights derived from the curvature map property. A multi-scale approach is used to minimize the dependence on user defined parameters. We show that by combining curvature maps and graph cuts in a multi-scale Type of Report: Other Department of Computer Science & Engineering Washington University in St. Louis Campus Box 1045 St. Louis, MO 63130 ph: (314) 935-6160 Tech report WUCSE-2006-22: Feature Detection Using Curvature Maps and the Min-Cut/Max-Flow Graph Cut Algorithm Timothy Gatzke and Cindy Grimm Washington University in St. Louis, St. Louis MO 63130, USA Abstract. Automatic detection of features in three-dimensional objects is a critical part of shape matching tasks such as object registration and recognition. Previous approaches to local surface matching have either focused on man-made objects, where features are generally well-defined, or required some type of user interaction to select features. Manual selection of corresponding features and subjective determination of the difference between objects are time consuming processes requiring a high level of expertise. Curvature is a useful property of a surface, but curvature calculation on a discrete mesh is often noisy and not always accurate. However, the Curvature Map, which represents shape information for a point and its surrounding region, is robust with respect to grid resolution and mesh regularity. It can be used as a measure of local surface similarity. We use these curvature map properties to extract features and segment the surface accordingly. Although thresholding techniques can be used to generate reasonable features, the choice of a threshold is very subjective and the results may be very sensitive to this choice. To avoid the threshold dilemma and to make the selection of the feature region less subjective, we employ a min-cut/max-flow graph cut algorithm, with vertex weights derived from the curvature map property. A multi-scale approach is used to minimize the dependence on user defined parameters. We show that by combining curvature maps and graph cuts in a multi-scale framework, we can extract meaningful features in a robust way. Automatic detection of features in three-dimensional objects is a critical part of shape matching tasks such as object registration and recognition. Previous approaches to local surface matching have either focused on man-made objects, where features are generally well-defined, or required some type of user interaction to select features. Manual selection of corresponding features and subjective determination of the difference between objects are time consuming processes requiring a high level of expertise. Curvature is a useful property of a surface, but curvature calculation on a discrete mesh is often noisy and not always accurate. However, the Curvature Map, which represents shape information for a point and its surrounding region, is robust with respect to grid resolution and mesh regularity. It can be used as a measure of local surface similarity. We use these curvature map properties to extract features and segment the surface accordingly. Although thresholding techniques can be used to generate reasonable features, the choice of a threshold is very subjective and the results may be very sensitive to this choice. To avoid the threshold dilemma and to make the selection of the feature region less subjective, we employ a min-cut/max-flow graph cut algorithm, with vertex weights derived from the curvature map property. A multi-scale approach is used to minimize the dependence on user defined parameters. We show that by combining curvature maps and graph cuts in a multi-scale framework, we can extract meaningful features in a robust way.