Learning metric graphs for neuron segmentation in electron microscopy images

Kyle Luther, H. Sebastian Seung

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


In the deep metric learning approach to image segmentation, a convolutional net densely generates feature vectors at the pixels of an image. Pairs of feature vectors are trained to be similar or different, depending on whether the corresponding pixels belong to same or different ground truth segments. To segment a new image, the feature vectors are computed and clustered. Both empirically and theoretically, it is unclear whether or when deep metric learning is superior to the more conventional approach of directly predicting an affinity graph with a convolutional net. We compare the two approaches using brain images from serial section electron microscopy images, which constitute an especially challenging example of instance segmentation. We first show that seed-based postprocessing of the feature vectors, as originally proposed, produces inferior accuracy because it is difficult for the convolutional net to predict feature vectors that remain uniform across large objects. Then we consider postprocessing by thresholding a nearest neighbor graph followed by connected components. In this case, segmentations from a 'metric graph' turn out to be competitive or even superior to segmentations from a directly predicted affinity graph. To explain these findings theoretically, we invoke the property that the metric function satisfies the triangle inequality. Then we show with an example where this constraint suppresses noise, causing connected components to more robustly segment a metric graph than an unconstrained affinity graph.

Original languageEnglish (US)
Title of host publicationISBI 2019 - 2019 IEEE International Symposium on Biomedical Imaging
PublisherIEEE Computer Society
Number of pages5
ISBN (Electronic)9781538636411
StatePublished - Apr 2019
Event16th IEEE International Symposium on Biomedical Imaging, ISBI 2019 - Venice, Italy
Duration: Apr 8 2019Apr 11 2019

Publication series

NameProceedings - International Symposium on Biomedical Imaging
ISSN (Print)1945-7928
ISSN (Electronic)1945-8452


Conference16th IEEE International Symposium on Biomedical Imaging, ISBI 2019

All Science Journal Classification (ASJC) codes

  • Biomedical Engineering
  • Radiology Nuclear Medicine and imaging


  • Image segmentation
  • Machine learning
  • Microscopy - electron


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