A Theory of Shape Identification

  • Frédéric Cao
  • José-Luis Lisani
  • Jean-Michel Morel
  • Pablo Musé
  • Frédéric Sur

Part of the Lecture Notes in Mathematics book series (LNM, volume 1948)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Extracting Image boundaries

  3. Level Line Invariant Descriptors

  4. Recognizing Level Lines

  5. Grouping Shape Elements

  6. The SIFT Method

  7. Back Matter
    Pages 225-257

About this book


Recent years have seen dramatic progress in shape recognition algorithms applied to ever-growing image databases. They have been applied to image stitching, stereo vision, image mosaics, solid object recognition and video or web image retrieval. More fundamentally, the ability of humans and animals to detect and recognize shapes is one of the enigmas of perception.

The book describes a complete method that starts from a query image and an image database and yields a list of the images in the database containing shapes present in the query image. A false alarm number is associated to each detection. Many experiments will show that familiar simple shapes or images can reliably be identified with false alarm numbers ranging from 10-5 to less than 10-300

Technically speaking, there are two main issues. The first is extracting invariant shape descriptors from digital images. The second  is deciding whether two shape descriptors are identifiable as the same shape or not. A perceptual principle, the Helmholtz principle, is the cornerstone of this decision.

These decisions rely on elementary stochastic geometry and compute a false alarm number. The lower this number, the more secure the identification. The description of the processes, the many experiments on digital images and the simple proofs of mathematical correctness are interlaced so as to make a reading accessible to various audiences, such as students, engineers, and researchers.


Stereo a contrario methods algorithms calculus cluster analysis cognition databases meaningful level lines object recognition scale invariant features shape grouping shape recognition stereo vision

Authors and affiliations

  • Frédéric Cao
    • 1
  • José-Luis Lisani
    • 2
  • Jean-Michel Morel
    • 3
  • Pablo Musé
    • 4
  • Frédéric Sur
    • 5
  1. 1.DxO LabsFrance
  2. 2.Dep. Matemàtiques i InformàticaUniversity Balearic IslandsBalearsSpain
  3. 3.Ecole Normale Supérieure de CachanCMLAFrance
  4. 4.Instituto de Ingeniería EléctricaUruguay
  5. 5.Loria Bat. C - projet Magrit Campus ScientifiqueFrance

Bibliographic information