Placental Vessel Extraction with Shearlets, Laplacian Eigenmaps, and a Conditional Generative Adversarial Network

  • Catalina AnghelEmail author
  • Kellie Archer
  • Jen-Mei Chang
  • Amy Cochran
  • Anca Radulescu
  • Carolyn M. Salafia
  • Rebecca Turner
  • Karamatou Yacoubou Djima
  • Lan Zhong
Part of the Association for Women in Mathematics Series book series (AWMS, volume 14)


The placenta is the key organ of maternal–fetal interactions, where nutrient, oxygen, and waste transfer take place. Differences in the morphology of the placental chorionic surface vascular network (PCSVN) have been associated with developmental disorders such as autism, hinting that the PCSVN could potentially serve as a biomarker for early diagnosis and treatment of autism. Studying PCSVN features in large cohorts requires a reliable and automated mechanism to extract the vascular networks. This paper presents two distinct methods for PCSVN enhancement and extraction. Our first algorithm, which builds upon a directional multiscale mathematical framework based on a combination of shearlets and Laplacian eigenmaps, is able to intensify the appearance of vessels with high success in high-contrast images such as those produced in CT scans. Our second algorithm, which applies a conditional generative adversarial neural network (cGAN), was trained to simulate a human-traced PCSVN given a digital photograph of the placental chorionic surface. This method surpasses any existing automated PCSVN extraction methods reported on digital photographs of placentas. We hypothesize that a suitable combination of the two methods could further improve PCSVN extraction results and should be studied in the future.


Placenta Autism Vascular networks Shearlets Wavelets Laplacian eigenmaps Neural networks Deep learning cGAN Generative models 



The project was part of the MBI Women Advancing Mathematical Biology: Understanding Complex Biological Systems with Mathematics 2017 Workshop organized by the Association for Women in Mathematics. Funding for the workshop was provided by MBI, NSF ADVANCE “Career Advancement for Women Through Research-Focused Networks” (NSF-HRD 1500481), Society for Mathematical Biology, and Microsoft Research.

Over the course of the project, we received biology expertise and support from Drs. Ruchit Shah, George Merz, and Richard K. Miller.

The authors also wish to thank the following people who contributed to the collection of the placentas in the National Children’s Study Placenta Consortium: C.J. Stodgell, L. Salamone, L.I. Ruffolo, A. Penmetsa, P. Weidenborner (University of Rochester), J. Culhane, S. Wadlinger, M. Pacholski, M.A. Kent, L. Green (University of Pennsylvania), R. Wapner, C. Torres, J. Perou (Columbia University), P. Landrigan, J. Chen, L. Lambertini, L. Littman, P. Sheffield, A. Golden, J. Gilbert, C. Lendor, S. Allen, K. Mantilla, Y. Ma (Ichan School of Medicine), S. Leuthner, S. Szabo (Medical College of Wisconsin), J.L. Dalton, D. Misra (Placental Analytics), N. Thiex, K.Gutzman, A. Martin, B. Specker (South Dakota University), J. Swanson, C. Holliday, J. Butler (University of California at Irvine), A. Li, R.M.A.P.S. Dassanayake, J. Nanes, Y. Xia (University of Illinois at Chicago), J.C. Murray, T.D. Busch, J. Rigdon (University of Iowa), Kjersti Aagaard, A. Harris (Baylor College of Medicine), T.H. Darrah, E. Campbell (Boston University), N. Dole, J. Thorp, B. Eucker, C. Bell (University of North Carolina at Chapel Hill), E.B. Clark, M.W. Varner, E. Taggart, J. Billy, S. Stradling, J. Leavitt, W. Bell, S. Waterfall (University of Utah), B. O’Brien, M. Layton, D. Todd, K. Wilson, M.S. Durkin, M.-N. Sandoval (Westat, Inc).

Most importantly, we thank the study participants who donated their placentas.


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Copyright information

© The Author(s) and the Association for Women in Mathematics 2018

Authors and Affiliations

  • Catalina Anghel
    • 1
    Email author
  • Kellie Archer
    • 2
  • Jen-Mei Chang
    • 3
  • Amy Cochran
    • 4
  • Anca Radulescu
    • 5
  • Carolyn M. Salafia
    • 6
  • Rebecca Turner
    • 7
  • Karamatou Yacoubou Djima
    • 8
  • Lan Zhong
    • 9
  1. 1.University of California DavisDavisUSA
  2. 2.The Ohio State UniversityColumbusUSA
  3. 3.California State University Long BeachLong BeachUSA
  4. 4.University of WisconsinMadisonUSA
  5. 5.SUNY New PaltzNew PaltzUSA
  6. 6.Placental Analytics, LLC.New RochelleUSA
  7. 7.The University of AucklandAucklandNew Zealand
  8. 8.Amherst CollegeAmherstUSA
  9. 9.University of DelawareNewarkUSA

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