Local Frequency Descriptor (Volumetric)

In READ we used LFD to compute local gradient in 2D images. In this work we extend it to compute gradient in 3D volumetric data. First, we sample on a sphere around each voxel:

The Local Frequency Descriptor Gradient (LFDG) operator is the defined:

where . is the angle between an arbitrary axis (a) and sample k and the samples are located on a sphere

of radius R.

We construct a local coordinate system (i,j,k) by considering the 2D gradients computed in XY, XZ, and YZ planes (V1, V2, V3):

Finally, we quantize the 3D gradients computed by LFDG on the local coordinate system using 3D bins:

See the following reference for details:

Maani, Rouzbeh, Sanjay Kalra, and Yee-Hong Yang, "Robust volumetric texture classification of magnetic resonance images of the brain using local frequency descriptor." IEEE Transactions on Image Processing, 23.10 (2014): 4625-4636.

You can download the Matlab implementation from here [code]. Please cite the above reference if you use this code.