title: A novel measure and significance testing in data analysis of cell image segmentation.
abstract: BACKGROUND
  Cell image segmentation (CIS) is an essential part of quantitative imaging of biological cells. Designing a performance measure and conducting significance testing are critical for evaluating and comparing the CIS algorithms for image-based cell assays in cytometry. Many measures and methods have been proposed and implemented to evaluate segmentation methods. However, computing the standard errors (SE) of the measures and their correlation coefficient is not described, and thus the statistical significance of performance differences between CIS algorithms cannot be assessed.
  
  
  RESULTS
  We propose the total error rate (TER), a novel performance measure for segmenting all cells in the supervised evaluation. The TER statistically aggregates all misclassification error rates (MER) by taking cell sizes as weights. The MERs are for segmenting each single cell in the population. The TER is fully supported by the pairwise comparisons of MERs using 106 manually segmented ground-truth cells with different sizes and seven CIS algorithms taken from ImageJ. Further, the SE and 95% confidence interval (CI) of TER are computed based on the SE of MER that is calculated using the bootstrap method. An algorithm for computing the correlation coefficient of TERs between two CIS algorithms is also provided. Hence, the 95% CI error bars can be used to classify CIS algorithms. The SEs of TERs and their correlation coefficient can be employed to conduct the hypothesis testing, while the CIs overlap, to determine the statistical significance of the performance differences between CIS algorithms.
  
  
  CONCLUSIONS
  A novel measure TER of CIS is proposed. The TER's SEs and correlation coefficient are computed. Thereafter, CIS algorithms can be evaluated and compared statistically by conducting the significance testing.
authors.affiliation: National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA. jinchu.wu@nist.gov.
authors.forename: Jin Chu
authors.identifier: http://orcid.org/0000-0002-6340-2467
authors.initials: JC
authors.lastname: Wu
authors.affiliation: National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Halter
authors.affiliation: National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.
authors.forename: Raghu N
authors.initials: RN
authors.lastname: Kacker
authors.affiliation: National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.
authors.forename: John T
authors.initials: JT
authors.lastname: Elliott
authors.affiliation: National Institute of Standards and Technology, Gaithersburg, MD, 20899, USA.
authors.forename: Anne L
authors.initials: AL
authors.lastname: Plant
mesh_terms: D000465:Algorithms; D000818:Animals; D007090:Image Interpretation, Computer-Assisted; D051379:Mice; D008856:Microscopy, Fluorescence; D032389:Myocytes, Smooth Muscle / Q000166:cytology
keywords: Bootstrap method; Cell assays; Cell image segmentation; Confidence interval; Correlation coefficient; Misclassification error rate; Performance measure; Significance testing; Standard error; Total error rate