Research Projects

The research presents a new method for designing neural networks that remain equivariant to elastic transformations, which are non-linear deformations found in real-world datasets. Elastic transformations are represented as mappings from one image space to another, guided by a deformation field. The goal is to produce outputs that mirror the transformation of the input. The "elastic-equivariant convolution" uses a deformation-invariant kernel to achieve this. The training of the network relies on an objective function that ensures model equivariance to elastic transformations. Riemannian gradient descent optimization algorithms are used to address the complex nature of this objective. The research also uses the Large Deformation Diffeomorphic Metric Mapping framework to capture image deformations. The aim is to create neural networks that are inherently resilient to non-linear image deformations.