KEYWORDS: LIDAR, Matrices, 3D image processing, Image segmentation, 3D modeling, 3D acquisition, Principal component analysis, Visualization, Data modeling, Vector spaces
Manifold extraction techniques, such as ISOMAP, are capable of projecting nonlinear, high-dimensional data to a lower-dimensional
subspace while retaining discriminatory information. In this investigation, ISOMAP is applied to 3D
LADAR range imagery. Selected man-made objects are reduced to sets of spin-image feature vectors that describe object
surface geometries. At various spin-image support scales, we use the distribution-free Henze-Penrose statistic test to
quantify differences between man-made objects in both the high-dimensional spin-image vector representation and in the
low-dimensional spin-image manifold extracted using ISOMAP.
Spin images originated within the robotics group at Carnegie Mellon University and are representations of 3-space surface regions. This representation provides a means for surface matching that is invariant to rigid body rotations and translations while being robust in the presence of 3D image noise, clutter, and surface occlusion. Of particular interest is the viability of using spin images to differentiate between two object classes in 3D imagery where there is significant intra-class diversity, e.g. to differentiate between wheeled and tracked vehicles. The specificity of spin map representations in differentiation of wheeled and tracked vehicles is statistically characterized. Using synthetic imagery of various wheeled and tracked vehicles, the class separability of wheeled vs. tracked vehicle spin image sets is nonparametrically quantified via entropic characterization as well as the Friedman-Rafsky two-sample test statistic. Additionally, class separability is analyzed in lower dimensional feature spaces generated via the Hotelling transform as well as a random projection method, comparing and contrasting the spin map class differentiation in the original and transformed data sets.
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