Distance measures for image segmentation evaluation

The task considered in this paper is performance evaluation of region segmentation algorithms in the ground-truth-based paradigm. Given a machine segmentation and a ground-truth segmentation, performance measures are needed. We propose to consider the image segmentation problem as one of data clustering and, as a consequence, to use measures for comparing clusterings developed in statistics and machine learning. By doing so, we obtain a variety of performance measures which have not been used before in image processing. In particular, some of these measures have the highly desired property of being a metric. Experimental results are reported on both synthetic and real data to validate the measures and compare them with others.

Fitting of Mixtures with Unspecified Number of Components Using Cross Validation Distance Estimate

Estimation of the number of mixture components (k) is an unsolved problem. Available methods for estimation of k include bootstrapping the likelihood ratio test statistics and optimizing a variety of validity functionals such as AIC, BIC/MDL, and ICOMP. We investigate the minimization of distance between fitted mixture model and the true density as a method for estimating k. The distances considered are Kullback-Leibler (KL) and “L sub 2”. We estimate these distances using cross validation. A reliable estimate of k is obtained by voting of B estimates of k corresponding to B cross validation estimates of distance. This estimation methods with KL distance is very similar to Monte Carlo cross validated likelihood methods discussed by Smyth (2000). With focus on univariate normal mixtures, we present simulation studies that compare the cross validated distance method with AIC, BIC/MDL, and ICOMP. We also apply the cross validation estimate of distance approach along with AIC, BIC/MDL and ICOMP approach, to data from an osteoporosis drug trial in order to find groups that differentially respond to treatment.

Ultrasound measurements of the distance between acupuncture needle tip at P6 and the median nerve

BACKGROUND: Pericard 6 (P6) is one of the most frequently used acupuncture points, especially in preventing nausea and vomiting. At this point, the median nerve is located very superficially. OBJECTIVES: To investigate the distance between the needle tip and the median nerve during acupuncture at P6, we conducted a prospective observational ultrasound (US) imaging study. We tested the hypothesis that de qi (a sensation that is typical of acupuncture needling) is evoked when the needle comes into contact with the epineural tissue and thereby prevents nerve penetration. SETTINGS/LOCATION: The outpatient pain clinic of the Medical University of Vienna, Austria. SUBJECTS: Fifty (50) patients receiving acupuncture treatment including P6 bilaterally. INTERVENTIONS: Patients were examined at both forearms using US (a 10-MHz linear transducer) after insertion of the needle at P6. OUTCOME MEASURES: The distance between the needle tip and the median nerve, the number of nerve contacts and nerve penetrations, as well as the number of successfully elicited de qi sensations were recorded. RESULTS: Complete data could be obtained from 97 cases. The mean distance from the needle tip to the nerve was 1.8 mm (standard deviation 2.2; range 0-11.3). Nerve contacts were recorded in 52 cases, in 14 of which the nerve was penetrated by the needle. De qi was elicited in 85 cases. We found no association between the number of nerve contacts and de qi. The 1-week follow-up showed no complications or neurologic problems. CONCLUSIONS: This is the first investigation demonstrating the relationship between acupuncture needle placement and adjacent neural structures using US technology. The rate of median nerve penetrations by the acupuncture needle at P6 was surprisingly high, but these seemed to carry no risk of neurologic sequelae. De qi at P6 does not depend on median nerve contact, nor does it prevent median nerve penetration.