Estimation of neuronal firing rates with the three-state biological point process model.

In the subcortex of the human brain, neuronal firing events are stochastic and the inter-arrival times of action potentials (APs) are highly irregular. It has been shown that stimulation of the subthalamic nucleus (STN), a small subcortical structure located within the basal ganglia, can help ameliorate the motor symptoms associated with Parkinson's disease (PD). However, success of image guided stereotactic surgery is reliant upon the refinement of the anatomic target (in this case the STN) based on micro-electrode recordings (MERs) of background activity and firing rate. In practice MERs must be analysed on-line and in real-time. Currently, the most common method of performing on-line MER analysis is a manual thresholding procedure. However, this is subjective in nature and often complicated by the presence of variable amounts of background noise. Therefore, in this paper, we present an automated adaptive thresholding technique, based on a modified 'top-hat' operator, which detects APs exceeding the local background activity. We then go on to model these inter-arrival times using a coupled Poisson process that provides improved estimates of both inter-burst and intra-burst neuronal firing activity in the STN.

Maximum-likelihood estimation of circle parameters via convolution.

The accurate fitting of a circle to noisy measurements of circumferential points is a much studied problem in the literature. In this paper, we present an interpretation of the maximum-likelihood estimator (MLE) and the Delogne-Kåsa estimator (DKE) for circle-center and radius estimation in terms of convolution on an image which is ideal in a certain sense. We use our convolution-based MLE approach to find good estimates for the parameters of a circle in digital images. In digital images, it is then possible to treat these estimates as preliminary estimates into various other numerical techniques which further refine them to achieve subpixel accuracy. We also investigate the relationship between the convolution of an ideal image with a "phase-coded kernel" (PCK) and the MLE. This is related to the "phase-coded annulus" which was introduced by Atherton and Kerbyson who proposed it as one of a number of new convolution kernels for estimating circle center and radius. We show that the PCK is an approximate MLE (AMLE). We compare our AMLE method to the MLE and the DKE as well as the Cramér-Rao Lower Bound in ideal images and in both real and synthetic digital images.