Skip to content
Register Sign in Wishlist

Geometric and Topological Inference

$46.99 (P)

Part of Cambridge Texts in Applied Mathematics

  • Date Published: September 2018
  • availability: In stock
  • format: Paperback
  • isbn: 9781108410892

$ 46.99 (P)

Add to cart Add to wishlist

Other available formats:
Hardback, eBook

Looking for an examination copy?

If you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.

    • Establishes a trajectory from basic combinatorial and simplicial topology all the way to persistent homology
    • Illustrates numerous established techniques with thorough treatment
    • This book has been classroom tested, and written by distinguished researchers of international stature
    Read more

    Reviews & endorsements

    'How do you make sense of a cloud of points in high dimension? This book will tell you. Be ready for a merry ride through the awesome canyons of geometry and topology with, ever lurking in the shadows, the dreaded curse of dimensionality. Destined to become an instant classic, this book treats its reader to a gentle introduction to the subject while providing a laser-sharp focus on the hottest topics of the day. For students and researchers alike, this delightful volume will be the go-to reference in the field of geometric inference.' Bernard Chazelle, Princeton University, New Jersey

    'Problems related to understanding the relationship between a space and points sampled from within it - perhaps with noise and perhaps not too densely - are important in areas ranging from data analysis, approximation theory, and graphics to differential geometry and topology. This book emphasizes the algorithmic side of the subject explaining both classical and recent ideas carefully and clearly. While not encyclopedic, it is the finest kind of exposition: masters of the field have picked and explained a number of the most important ideas, many of which are scattered in the research literature, building a vantage point from which the reader can explore the broad terrain of applications, refinements, and variations.' Shmuel Weinberger, University of Chicago

    'Rooted in geometry and topology, the problem of inferring a shape from its point-samples is at the heart of many applications in science and engineering. In the past two decades, researchers, primarily in the field of computational geometry, have studied this problem from the viewpoint of designing algorithms with certified guarantees. Written by three experts in the field, this book epitomizes these research efforts. By focusing on high dimensions, the authors offer views complementary to recent learning techniques.' Tamal K. Dey, Ohio State University

    ‘So it is fair to say that this book scores high marks on a number of counts. Not only does it address very sexy and fecund contemporary material that bridges pure and applied mathematics is a way heretofore hardly imaginable … it is of considerable pedagogical use. The reader gets airborne quickly and gets to fly pretty high.’ Michael Berg, MAA Reviews

    ‘… it is clear that this book addresses issues that are likely to be of some interest to budding researchers. I suspect that it provides them with as accessible an introduction to this material as is currently available.’ Mark Hunacek, The Mathematical Gazette

    See more reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: September 2018
    • format: Paperback
    • isbn: 9781108410892
    • length: 246 pages
    • dimensions: 229 x 153 x 14 mm
    • weight: 0.35kg
    • availability: In stock
  • Table of Contents

    Part I. Topological Preliminaries:
    1. Topological spaces
    2. Simplicial complexes
    Part II. Delaunay Complexes:
    3. Convex polytopes
    4. Delaunay complexes
    5. Good triangulations
    6. Delaunay filtrations
    Part III. Reconstruction of Smooth Submanifolds:
    7. Triangulation of submanifolds
    8. Reconstruction of submanifolds
    Part IV. Distance-Based Inference:
    9. Stability of distance functions
    10. Distance to probability measures
    11. Homology inference.

  • Authors

    Jean-Daniel Boissonnat, INRIA Sophia Antipolis
    Jean-Daniel Boissonnat is a Research Director at the Institut national de recherche en informatique et en automatique, France. His research interests are in computational geometry and topology. He has published several books and more than 180 research papers, and is on the editorial board of the Journal of the ACM and of Discrete and Computational Geometry. He received the IBM award in Computer Science in 1987, the EADS award in Information Sciences in 2006 and was awarded an advanced grant from the European Research Council in 2014. He has taught at several universities in Paris and at the Collège de France.

    Frédéric Chazal, Inria Saclay - Ile-de-France
    Frédéric Chazal is a Research Director at the Institut national de recherche en informatique et en automatique, France, where he is heading the DataShape team, a pioneering and world leading group in computational geometry and topological data analysis. His current primary research is on topological data analysis and its connections with statistics and machine learning, and he has authored several reference papers in this domain. He is an associate editor of four international journals and he teaches topological data analysis in various universities and engineering schools in the Paris area.

    Mariette Yvinec, INRIA Sophia Antipolis
    Mariette Yvinec was a Researcher at the Institut national de recherche en informatique et en automatique, France. She is a specialist in the field of shape reconstruction and meshing, and taught master's courses on the subject in various universities in Paris. She co-authored a reference book on computational geometry with Jean-Daniel Boissonnat, and played an active role in the design and development of the software library CGAL.

Related Books

also by this author

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.