An Approach to the Computation of the Euler Number by means of the Vertex Chain Code

<div>Complementary chains: (a) an example of a 2D shape and its outer vertices; (b) the complementary chain of the shape shown in (a). Now, this shape corresponds to a hole; (c) the set <span class="nowrap"><svg height="7.30254pt" id="M52" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -7.25272 7.75925 7.30254" width="7.75925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M574 548H512L295 69H293L76 548H14L263 0H325L574 548Z"></path></g></svg>,</span> i.e., <svg height="11.6425pt" id="M53" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 60.7745 11.6425" width="60.7745pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.798,0)"><path d="M535 194V548H477V194C477 102 391 35 294 35S111 102 111 194V548H53V194C53 72 166 -15 294 -15S535 72 535 194Z"></path></g><g transform="matrix(.013,0,0,-0.013,22.334,0)"><path d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,31.226,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.013,0,0,-0.013,38.654,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,49.917,0)"><path d="M574 548H512L295 69H293L76 548H14L263 0H325L574 548Z"></path></g><g transform="matrix(.013,0,0,-0.013,57.548,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></div>

Computational and Mathematical Methods in Medicine

fig4

Figure 4

Figure 4: An Approach to the Computation of the Euler Number by means of the Vertex Chain Code 