We demonstrate that isomorphically mapping gray-level medical image matrices onto energy spaces underlying the framework of fast data density functional transform (fDDFT) can achieve the unsupervised recognition of lesion morphology. By introducing the architecture of geometric deep learning and metrics of graph neural networks, gridized density functionals of the fDDFT establish an unsupervised feature-aware mechanism with global convolutional kernels to extract the most likely lesion boundaries and produce lesion segmentation. An AutoEncoder-assisted module reduces the computational complexity from [Formula: see text] to [Formula: see text], thus efficiently speeding up global convolutional operations. We validate their performance utilizing various open-access datasets and discuss limitations. The inference time of each object in large three-dimensional datasets is 1.76 s on average. The proposed gridized density functionals have activation capability synergized with gradient ascent operations, hence can be modularized and embedded in pipelines of modern deep neural networks. Algorithms of geometric stability and similarity convergence also raise the accuracy of unsupervised recognition and segmentation of lesion images. Their performance achieves the standard requirement for conventional deep neural networks; the median dice score is higher than 0.75. The experiment shows that the synergy of fDDFT and a naïve neural network improves the training and inference time by 58% and 51%, respectively, and the dice score raises to 0.9415. This advantage facilitates fast computational modeling in interdisciplinary applications and clinical investigation.
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