Fast 3D Image Moments

TL;DR

This paper introduces an efficient algorithm for computing 3D image moments that significantly reduces computational complexity by leveraging 2D projections, with applications in medical imaging like MRI and CT.

Contribution

The paper presents a novel algorithm that reduces the computational complexity of 3D moments from O(n^3) to O(n) using 2D projections, improving efficiency in volumetric image analysis.

Findings

Reduces processing time for 3D moments calculation

Effective in MRI and CT image analysis

Applicable to 3D object analysis from 2D images

Abstract

An algorithm to efficiently compute the moments of volumetric images is disclosed. The approach demonstrates a reduction in processing time by reducing the computational complexity significantly. Specifically, the algorithm reduces multiplicative complexity from O(n^3) to O(n). Several 2D projection images of the 3D volume are generated. The algorithm computes a set of 2D moments from those 2D images. Those 2D moments are then used to derive the 3D volumetric moments. Examples of use in MRI or CT and related analysis demonstrates the benefit of the Discrete Projection Moment Algorithm. The approach is also useful in computing the moments of a 3D object using a small set of 2D tomographic images of that object.