Differentiable Quadratic Regularization in Graphs Integrated with Convolutional Networks for Image Colorization

This research proposes a hybrid architecture for the colorization of grayscale images that integrates convolutional neural networks to a differentiable optimization layer based on quadratic regularization over pixel graphs. The U-Net network extracts luminance characteristics and estimates an initial chromaticity distribution and smoothing weights at the edges of the spatial grid. A differentiable quadratic programming layer (implemented via cvxpylayers) refines prediction by solving a convex problem that favors spatial coherence. The backpropagation of the gradients occurs by implicit differentiation of the optimum conditions. Assays in the CIFAR-10 set indicate improvements in MSE, PSNR, and SSIM compared to a convolutional baseline. The learned weights suggest spatial patterns associated with homogeneous regions and local discontinuities, indicating the potential of differentiable programming in the integration between optimization in graphs and deep learning.