  The contributions of this thesis stem from technology developed to analyse
large sets of volumetric images in terms of atom-like features extracted in 3D
image space, following SIFT algorithm in 2D image space. New feature properties
are introduced including a binary feature sign, analogous to an electrical
charge, and a discrete set of symmetric feature orientation states in 3D space.
These new properties are leveraged to extend feature invariance to include the
sign inversion and parity (SP) transform, analogous to the charge conjugation
and parity (CP) transform between a particle and its antiparticle in quantum
mechanics, thereby accounting for local intensity contrast inversion between
imaging modalities and axis reflections due to shape symmetry. A novel
exponential kernel is proposed to quantify the similarity of a pair of features
extracted in different images from their properties including location, scale,
orientation, sign and appearance. A novel measure entitled the soft Jaccard is
proposed to quantify the similarity of a pair of feature sets based on their
overlap or intersection-over-union, where a kernel establishes non-binary or
soft equivalence between a pair of feature elements. The soft Jaccard may be
used to identify pairs of feature sets extracted from the same individuals or
families with high accuracy, and a simple distance threshold led to the
surprising discovery of previously unknown individual and family labeling
errors in major public neuroimage datasets. A new algorithm is proposed to
register or spatially align a pair of feature sets, entitled SIFT Coherent
Point Drift (SIFT-CPD), by identifying a transform that maximizes the soft
Jaccard between a fixed feature set and a transformed set. SIFT-CPD achieves
faster and more accurate registration than the original CPD algorithm based on
feature location information alone, in a variety of challenging.
