Fast 3D Image Moments

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.

Efficient Computation of Higher Order 2D Image Moments using the Discrete Radon Transform

Geometric moments and moment invariants of image artifacts have many uses in computer vision applications, e.g. shape classification or object position and orientation. Higher order moments are of interest to provide additional feature descriptors, to measure kurtosis or to resolve n-fold symmetry. This paper provides the method and practical application to extend an efficient algorithm, based on the Discrete Radon Transform, to generate moments greater than the 3rd order. The mathematical fundamentals are presented, followed by relevant implementation details. Results of scaling the algorithm based on image area and its computational comparison with a standard method demonstrate the efficacy of the approach.

Using the discrete radon transformation for grayscale image moments

Image moments are weighted sums over pixel values in a given image and are used in object detection and localization. Raw image moments are derived directly from the image and are fundamental in deriving moment invariants quantities. The current general algorithm for raw image moments is computationally expensive and the number of multiplications needed scales with the number of pixels in the image. For an image of size (N,M), it has O(NM) multiplications. In this paper we outline an algorithm using the Discrete Radon Transformation for computing the raw image moments of a grayscale image. It reduces two dimensional moment calculations to linear combinations of one dimensional moment calculations. We show that the number of multiplications needed scales as O(N + M), making it faster then the most widely used algorithm of raw image moments.