Locally Connected Pyramid Representation for Instance Optimization in 3D Image Registration

We propose Locally Connected Pyramids for image registration (LCPReg), a light-weight neural displacement representation built specifically for pair-wise optimization. LCPReg explicitly optimizes only a coarse displacement field and carries it to image resolution through a cascade of learnable, locally connected upsampling layers. Each coarse site holds its own kernel, so the refinement can adapt to the local deformation, and each kernel is factorized into one-dimensional components, which keeps the parameter count to manageable numbers and encourages smooth transformations. We further introduce an approximate B-spline weight initialization scheme with warm start optimization that exactly reproduces a prior displacement estimate, allowing LCPReg to serve as a drop-in replacement in existing image registration pipelines. We integrate LCPReg into three frameworks (NODEO, convexAdam, and uniGradICON) and evaluate it on benchmark datasets (OASIS, CANDI and EMPIRE10). LCPReg consistently improves Dice scores over each framework's original representation with comparable regularity. It also substantially lowers optimization time for NODEO and uniGradICON.