Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Hierarchical Bayesian Approach to Image Restoration: Applications to Astronomical Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
An image analysis algorithm for dendritic spines
Neural Computation
A 3D 12-subiteration thinning algorithm based on P-simple points
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Monte Carlo Statistical Methods (Springer Texts in Statistics)
Generalizing Swendsen-Wang to Sampling Arbitrary Posterior Probabilities
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Experimental research seeking to quantify neuronal structure constantly contends with restrictions on image resolution and variability. In particular, experimentalists often need to analyze images with very low signal-to-noise ratio (SNR). In many experiments, dye toxicity scales with the light intensity; this leads experimentalists to reduce image SNR in order to preserve the viability of the specimen. In this paper, we present a Bayesian approach for estimating the neuronal shape given low-SNR observations. This Bayesian framework has two major advantages. First, the method effectively incorporates known facts about 1) the image formation process, including blur and the Poisson nature of image noise at low intensities, and 2) dendritic shape, including the fact that dendrites are simply-connected geometric structures with smooth boundaries. Second, we may employ standard Markov chain Monte Carlo techniques for quantifying the posterior uncertainty in our estimate of the dendritic shape. We describe an efficient computational implementation of these methods and demonstrate the algorithm's performance on simulated noisy two-photon laser-scanning microscopy images.