SummaryIn this paper, we compare the performance of three iterative methods for image restoration: the Richardson-Lucy algorithm, the iterative constrained Tikhonov-Miller algorithm (ICTM) and the Carrington algorithm. Both the ICTM and the Carrington algorithm are based on an additive Gaussian noise model, but differ in the way they incorporate the non-negativity constraint. Under low light-level conditions, this additive (Gaussian) noise model is a poor description of the actual photon-limited image recording, compared with that of a Poisson process. The RichardsonLucy algorithm is a maximum likelihood estimator for the intensity of a Poisson process. We have studied various methods for determining the regularization parameter of the ICTM and the Carrington algorithm and propose a (Gaussian) prefiltering to reduce the noise sensitivity of the Richardson-Lucy algorithm. The results of these algorithms are compared on spheres convolved with a point spread function and distorted by Poisson noise. Our simulations show that the Richardson-Lucy algorithm, with Gaussian prefiltering, produces the best result in most of the tests. Finally, we show an example of how restoration methods can improve quantitative analysis: the total amount of fluorescence inside a closed object is measured in the vicinity of another object before and after restoration.

We propose a new strategy to design recursive implementations of the Gaussian filter and Gaussian regularized derivative filters. Each recursive filter consists of a cascade of two stable N th -order subsystems (causal and anti-causal). The computational complexity is 2N multiplications per pixel per dimension independent of the size (σ) of the Gaussian kernel. The filter coefficients have a closed-form solution as a function of scale (σ) and recursion order N (N=3,4,5). The recursive filters yield a high accuracy and excellent isotropy in n-D space.

In this paper we present methods for characterizing CCD cameras. Interesting properties are linearity of photometric response, signal-to-noise ratio (SNR), sensitivity, dark current and spatial frequency response (SFR). The techniques to characterize CCD cameras are carefully designed to assist one in selecting a camera to solve a certain problem. The methods described were applied to a variety of cameras: an Astromed TE3/A with P86000 chip, a Photometrics CC200 series with Thompson chip TH7882, a Photometrics CC200 series with Kodak chip KAF1400, a Xillix' Micro Imager 1400 with Kodak chip KAF1400, an HCS MXR CCD with a Philips chip and a Sony XC-77RRCE.

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Background: Corneal endothelium (CE) images provide valuable clinical information regarding the health state of the cornea. Computation of the clinical morphometric parameters requires the segmentation of endothelial cell images. Current techniques to image the endothelium in vivo deliver low quality images, which makes automatic segmentation a complicated task. Here, we present two convolutional neural networks (CNN) to segment CE images: a global fully convolutional approach based on U-net, and a local sliding-window network (SW-net). We propose to use probabilistic labels instead of binary, we evaluate a preprocessing method to enhance the contrast of images, and we introduce a postprocessing method based on Fourier analysis and watershed to convert the CNN output images into the final cell segmentation. Both methods are applied to 50 images acquired with an SP-1P Topcon specular microscope. Estimates are compared against a manual delineation made by a trained observer. Results: U-net (AUC = 0.9938) yields slightly sharper, clearer images than SW-net (AUC = 0.9921). After postprocessing, U-net obtains a DICE = 0.981 and a MHD = 0.22 (modified Hausdorff distance), whereas SW-net yields a DICE = 0.978 and a MHD = 0.30. U-net generates a wrong cell segmentation in only 0.48% of the cells, versus 0.92% for the SW-net. U-net achieves statistically significant better precision and accuracy than both, Topcon and SW-net, for the estimates of three clinical parameters: cell density (ECD), polymegethism (CV), and pleomorphism (HEX). The mean relative error in U-net for the parameters is 0.4% in ECD, 2.8% in CV, and 1.3% in HEX. The computation time to segment an image and estimate the parameters is barely a few seconds. Conclusions: Both methods presented here provide a statistically significant improvement over the state of the art. U-net has reached the smallest error rate. We suggest a segmentation refinement based on our previous work to further improve the performance.