Solving Square Jigsaw Puzzle by Hierarchical Loop Constraints.

We present a novel computational puzzle solver for square-piece image jigsaw puzzles with no prior information such as piece orientation or anchor pieces. By "piece" we mean a square $d$d x $d$d block of pixels, where we investigate pieces as small as 7 × 7 pixels. To reconstruct such challenging puzzles, we propose to find maximum geometric consensus between pieces, specifically hierarchical piece loops. The proposed algorithm seeks out loops of four pieces and aggregates the smaller loops into higher order "loops of loops" in a bottom-up fashion. In contrast to previous puzzle solvers which aim to maximize compatibility measures between all pairs of pieces and thus depend heavily on the pairwise compatibility measures used, our approach reduces the dependency on the pairwise compatibility measures which become increasingly uninformative for small scales and instead exploits geometric agreement among pieces. Our contribution also includes an improved pairwise compatibility measure which exploits directional derivative information along adjoining boundaries of the pieces. We verify the proposed algorithm as well as its individual components with mathematical analysis and reconstruction experiments.

Neuron Image Analyzer: Automated and Accurate Extraction of Neuronal Data from Low Quality Images.

Image analysis software is an essential tool used in neuroscience and neural engineering to evaluate changes in neuronal structure following extracellular stimuli. Both manual and automated methods in current use are severely inadequate at detecting and quantifying changes in neuronal morphology when the images analyzed have a low signal-to-noise ratio (SNR). This inadequacy derives from the fact that these methods often include data from non-neuronal structures or artifacts by simply tracing pixels with high intensity. In this paper, we describe Neuron Image Analyzer (NIA), a novel algorithm that overcomes these inadequacies by employing Laplacian of Gaussian filter and graphical models (i.e., Hidden Markov Model, Fully Connected Chain Model) to specifically extract relational pixel information corresponding to neuronal structures (i.e., soma, neurite). As such, NIA that is based on vector representation is less likely to detect false signals (i.e., non-neuronal structures) or generate artifact signals (i.e., deformation of original structures) than current image analysis algorithms that are based on raster representation. We demonstrate that NIA enables precise quantification of neuronal processes (e.g., length and orientation of neurites) in low quality images with a significant increase in the accuracy of detecting neuronal changes post-stimulation.