We harness the energy minimization aspects of the quantum-dot cellular automata (QCA) computing model to synthesize QCA circuits to solve the vision problem of perceptual grouping. Unlike logic computing, vision computing problems are error-tolerant, but are hard to solve on existing computing platforms. The cost of failure of not finding the optimal solution is not high; even solutions that are close to optimal can suffice. The problem of perceptual grouping concerns with selecting, based on Gestaltic perceptual cues, salient subsets of low-level features, such as straight line boundary segments, that are most likely to belong to objects in the scene. We formulate a method to map this problem, which can be cast in terms of energy minimization, onto an arrangement of QCA cells. The QCA cells correspond to the straight lines, and the kink energies between them model the Gestaltic cue affinities. The magnitude of the polarizations of the QCA cells denote the saliency of the corresponding image features. We use classical multi-dimensional scaling (MDS) to synthesize the QCA cell layout. We demonstrate the ability of this arrangement to compute salient groups in real images by simulating the QCA layout using iterative, self consistent analysis, based on the Hartree-Fock approximation.
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