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The contributions of this thesis stem from technology developed to analyselarge sets of volumetric images in terms of atom-like features extracted in 3Dimage space, following SIFT algorithm in 2D image space. New feature propertiesare introduced including a binary feature sign, analogous to an electricalcharge, and a discrete set of symmetric feature orientation states in 3D space.These new properties are leveraged to extend feature invariance to include thesign inversion and parity (SP) transform, analogous to the charge conjugationand parity (CP) transform between a particle and its antiparticle in quantummechanics, thereby accounting for local intensity contrast inversion betweenimaging modalities and axis reflections due to shape symmetry. A novelexponential kernel is proposed to quantify the similarity of a pair of featuresextracted in different images from their properties including location, scale,orientation, sign and appearance. A novel measure entitled the soft Jaccard isproposed to quantify the similarity of a pair of feature sets based on theiroverlap or intersection-over-union, where a kernel establishes non-binary orsoft equivalence between a pair of feature elements. The soft Jaccard may beused to identify pairs of feature sets extracted from the same individuals orfamilies with high accuracy, and a simple distance threshold led to thesurprising discovery of previously unknown individual and family labelingerrors in major public neuroimage datasets. A new algorithm is proposed toregister or spatially align a pair of feature sets, entitled SIFT CoherentPoint Drift (SIFT-CPD), by identifying a transform that maximizes the softJaccard between a fixed feature set and a transformed set. SIFT-CPD achievesfaster and more accurate registration than the original CPD algorithm based onfeature location information alone, in a variety of challenging.

Using Atom-Like Local Image Features to Study Human Genetics and Neuroanatomy in Large Sets of 3D Medical Image Volumes