  Locally Rotation Invariant (LRI) operators have shown great potential in
biomedical texture analysis where patterns appear at random positions and
orientations. LRI operators can be obtained by computing the responses to the
discrete rotation of local descriptors, such as Local Binary Patterns (LBP) or
the Scale Invariant Feature Transform (SIFT). Other strategies achieve this
invariance using Laplacian of Gaussian or steerable wavelets for instance,
preventing the introduction of sampling errors during the discretization of the
rotations. In this work, we obtain LRI operators via the local projection of
the image on the spherical harmonics basis, followed by the computation of the
bispectrum, which shares and extends the invariance properties of the spectrum.
We investigate the benefits of using the bispectrum over the spectrum in the
design of a LRI layer embedded in a shallow Convolutional Neural Network (CNN)
for 3D image analysis. The performance of each design is evaluated on two
datasets and compared against a standard 3D CNN. The first dataset is made of
3D volumes composed of synthetically generated rotated patterns, while the
second contains malignant and benign pulmonary nodules in Computed Tomography
(CT) images. The results indicate that bispectrum CNNs allows for a
significantly better characterization of 3D textures than both the spectral and
standard CNN. In addition, it can efficiently learn with fewer training
examples and trainable parameters when compared to a standard convolutional
layer.
