Author(s): Jean Serra
Year: 1983
Language: English
Pages: 620
Contents......Page 0009_0001.djvu
Preface......Page 0003_0001.djvu
Notation......Page 0013_0001.djvu
Part One: The Tools......Page 0017_0001.djvu
A. How to quantify the description of a structure......Page 0018_0001.djvu
B. The four principles of quantification......Page 0021_0001.djvu
C. Mathematical morphology......Page 0030_0001.djvu
D. Euclidean criteria and algorithms......Page 0035_0001.djvu
E. Models......Page 0039_0001.djvu
G. "Pravda" or "Istina"?......Page 0046_0001.djvu
A. Why this chapter heading?......Page 0049_0001.djvu
B. "One, two, three... infinity"......Page 0050_0001.djvu
C. The Hit or Miss transformation: an algebraic study......Page 0058_0001.djvu
D. Opening and closing......Page 0065_0001.djvu
E. Erosions and increasing mappings, morphological and algebraic openings......Page 0070_0001.djvu
F. A classification of the structuring elements......Page 0072_0001.djvu
G. Exercises......Page 0074_0001.djvu
A. What good is a topology?......Page 0078_0001.djvu
B. Review of topology......Page 0081_0001.djvu
C. The Hausdorff metric......Page 0087_0001.djvu
D. Topological structure for the closed sets of R^n......Page 0089_0001.djvu
E. Physical consequences of the Hit or Miss topology......Page 0098_0001.djvu
F. Topological properties of the Hit or Miss transformation......Page 0100_0001.djvu
G. Exercises......Page 0105_0001.djvu
A. A basic model......Page 0108_0001.djvu
B. Set properties of the convex sets......Page 0110_0001.djvu
C. The global point of view: integral geometry for compact convex sets......Page 0117_0001.djvu
D. Minkowski measures......Page 0129_0001.djvu
E. Convex sets and anisotropies......Page 0132_0001.djvu
F. Exercises......Page 0139_0001.djvu
A. Degrees of irregularity......Page 0142_0001.djvu
B. The convex ring and its extension......Page 0147_0001.djvu
C. The regular model......Page 0159_0001.djvu
D. The class K and fractal dimensions......Page 0161_0001.djvu
E. Exercises......Page 0173_0001.djvu
Part Two: Partial Knowledge......Page 0177_0001.djvu
A. Introduction......Page 0178_0001.djvu
B. Modules and the associated morphology......Page 0179_0001.djvu
C. Grids and rotations......Page 0185_0001.djvu
D. Grids and digital graphs......Page 0192_0001.djvu
E. Digital metrics and the associated morphology......Page 0201_0001.djvu
F. Digital morphology in Z^3......Page 0208_0001.djvu
G. Exercises......Page 0213_0001.djvu
A. Representations......Page 0220_0001.djvu
B. The digitalization concept......Page 0224_0001.djvu
C. Digitalizable transformations for the class (F)......Page 0227_0001.djvu
D. Homotopy and digitalization......Page 0229_0001.djvu
E. Convexity and digitalization......Page 0231_0001.djvu
F. Minkowski functionals and digitalization......Page 0233_0001.djvu
G. Conclusions......Page 0236_0001.djvu
H. Exercises......Page 0237_0001.djvu
A. Introduction......Page 0244_0001.djvu
B. Situation I......Page 0250_0001.djvu
C. Situation II......Page 0257_0001.djvu
D. Situation III......Page 0262_0001.djvu
E. Situation IV......Page 0265_0001.djvu
F. Situation V......Page 0273_0001.djvu
G. Conclusion......Page 0275_0001.djvu
H. Exercises......Page 0276_0001.djvu
Part Three: The Criteria......Page 0279_0001.djvu
A. A simple, but effective, tool......Page 0282_0001.djvu
B. Morphological properties......Page 0283_0001.djvu
C. A few algorithms......Page 0291_0001.djvu
D. A few probabilistic models......Page 0298_0001.djvu
E. A few examples......Page 0307_0001.djvu
F. Exercises......Page 0321_0001.djvu
A. What does "size" mean?......Page 0329_0001.djvu
B. 1-D size distributions......Page 0334_0001.djvu
C. Opening, closing, and size distribution in R^n......Page 0344_0001.djvu
D. Size distribution and individuals......Page 0355_0001.djvu
E. Spherical particles......Page 0361_0001.djvu
F. Theoretical complements......Page 0367_0001.djvu
G. Exercises......Page 0371_0001.djvu
A. Introduction......Page 0384_0001.djvu
B. The skeleton and maximum disks in R^n......Page 0386_0001.djvu
C. Medial axis and derivations of the skeleton......Page 0392_0001.djvu
D. Digitalization of the skeleton......Page 0398_0001.djvu
E. Thinnings and thickenings......Page 0401_0001.djvu
F. Homotopic thinnings and thickenings......Page 0406_0001.djvu
G. Connected components analysis......Page 0412_0001.djvu
H. Examples......Page 0419_0001.djvu
I. Exercises......Page 0427_0001.djvu
A. From sets to functions......Page 0435_0001.djvu
B. General results......Page 0436_0001.djvu
C. Transformations based on one cross-section......Page 0440_0001.djvu
D. Transformations based on two cross-sections......Page 0445_0001.djvu
E. Connectivity criteria......Page 0456_0001.djvu
F. From functions to sets: segmentation by watersheds......Page 0467_0001.djvu
G. Convexity and integral geometry......Page 0475_0001.djvu
H. Random functions......Page 0479_0001.djvu
I. Exercises......Page 0482_0001.djvu
Part Four: The Random Models......Page 0490_0001.djvu
A. Introduction......Page 0491_0001.djvu
B. The Boolean model......Page 0494_0001.djvu
C. Models derived from Boolean sets......Page 0512_0001.djvu
D. Poisson tesselation......Page 0522_0001.djvu
E. Other tesselations......Page 0530_0001.djvu
F. Point models......Page 0540_0001.djvu
G. Random sets......Page 0555_0001.djvu
H. The rose of models......Page 0562_0001.djvu
I. Exercises......Page 0563_0001.djvu
A. Judicious use of probabilistic models......Page 0586_0001.djvu
B. Mathematical models in morphology......Page 0593_0001.djvu
C. Pattern recognition modelling......Page 0594_0001.djvu
Appendix......Page 0598_0001.djvu
Bibliography......Page 0600_0001.djvu
Index......Page 0613_0001.djvu
