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.
KEYWORDS: 3D acquisition, LIDAR, 3D modeling, Automatic target recognition, Data modeling, Clouds, Chemical elements, 3D metrology, Solid modeling, Data compression
Three-dimensional (3D) Laser Detection and Ranging (LADAR) range data is being investigated for automatic target
recognition applications. The spin-image provides a useful data representation for 3D point cloud data. In the spirit of
recent work that shows ℓ1-sparseness to be a useful data compression metric, we propose to use Nonnegative Matrix
Factorization (NMF) to help find features that capture the salient information resident in the spin-image representation.
NMF is a technique for decomposing nonnegative multivariate data into its 'parts', resulting in a compressed and usually
sparse representation. As a surrogate for measured 3D LADAR data, we generate 3D point clouds from computer-aided-design
models of two land targets, and we generate spin-images at multiple support scales. We select the support scale
that provides the highest separability between the spin-image stacks from the two land targets. We then apply NMF to
the spin-images at this support scale, and seek elements corresponding to meaningful parts of the land vehicles (e.g., a
tank turret or truck wheels), that in a joint sense should provide significant discriminative capability. We measure the
separability in the sparse NMF subspace. For measuring separability, we use the Henze-Penrose measure of multivariate
distributional divergence.
The 'curse of dimensionality' has limited the application of statistical modeling techniques to low-dimensional spaces, but typical data usually resides in high-dimensional spaces (at least initially, for instance images represented as arrays of pixel values). Indeed, approaches such as Principal Component Analysis and Independent Component Analysis attempt to extract a set of meaningful linear projections while minimizing interpoint distance distortions. The counterintuitive yet effective random projections approach of Johnson and Lindenstrauss defines a sample-based dimensionality reduction technique with probabilistically provable distortion bounds. We investigate and report on the relative efficacy of two random projection techniques for Synthetic Aperture Radar images in a classification setting.
This investigation discusses the challenge of target classification in terms of intrinsic dimensionality estimation and selection of appropriate feature manifolds with object-specific classifier optimization. The feature selection process will be developed via nonlinear characterization and extraction of the target-conditional manifolds derived from the training data. We investigate defining the feature space used for classification as a class-conditioned nonlinear embedding, i.e., each training and test image is embedded in a target-specific embedding and the resultant embeddings are used for statistical characterization. We compare and contrast this novel embedding technique with Principal Component Analysis. The α-Jensen Entropy Difference measure is used to quantify the object-conditioned separation between the target distributions in the feature spaces. We discuss and demonstrate the effect of feature space extraction on classification efficacy.
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