A Multiobjective Approach to Homography Estimation

<table class="algorithm-group"><tr><td><table class="algorithm" id="pseudo1"><tr><td colspan="2">(1) for <svg height="8.8423pt" id="M26" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 24.8487 8.8423" width="24.8487pt" 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="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="273" vert-adv-y="273"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,7.181,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,18.444,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data></g></svg> through <svg height="8.8423pt" id="M27" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 9.02496 8.8423" width="9.02496pt" 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" id="g113-72"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="684" vert-adv-y="684"></glyph.data></g></svg></td></tr><tr><td colspan="2">(2)  Randomly select a subsample from <svg height="11.9218pt" id="M28" style="vertical-align:-3.181499pt" version="1.1" viewbox="-0.0498162 -8.7403 58.7915 11.9218" width="58.7915pt" 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="M442 495C434 557 427 602 423 639C405 645 348 665 284 665C142 665 55 579 55 469C55 373 127 319 229 267C304 227 348 190 348 131C348 67 309 25 248 25C152 25 93 138 73 202L38 190C45 130 58 46 68 21C81 15 100 7 128 -1C158 -10 193 -15 229 -15C375 -15 472 74 472 188C472 287 400 343 295 394C207 439 171 470 171 525C171 583 212 624 268 624C349 624 387 550 407 487L442 495Z" id="g13-81"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.565,3.132)"><path d="M151 515C194 515 227 548 227 587C227 629 194 661 152 661C112 661 77 629 77 587C77 548 112 515 151 515ZM290 0V39C230 46 226 52 226 120V457C172 442 105 428 38 421V386C88 379 95 376 95 309V120C95 49 89 45 31 39V0H290Z" id="g22-103"></path><glyph.data ascent="1041" descent="-369" horiz-adv-x="302" vert-adv-y="302"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,13.454,0)"><path d="M512 1V51H381C244 51 133 142 133 255S244 459 381 459H512V509H382C213 509 75 395 75 255S213 1 382 1H512Z" id="g117-77"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,24.716,0)"><path d="M703 311H403V276C508 267 513 259 513 189V94C513 63 505 47 490 38C477 29 454 26 434 26C270 26 196 184 196 335C196 515 300 623 420 623C514 623 589 576 613 464L651 472C643 550 638 603 635 637C599 645 522 665 440 665C229 665 44 546 44 318C44 117 193 -15 425 -15C506 -15 593 7 653 21C648 47 647 79 647 115V195C647 262 653 266 703 276V311Z" id="g13-69"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="727" vert-adv-y="727"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,37.799,0)"><path d="M531 95V145H339C215 145 115 224 115 322S215 500 339 500H531V550H338C183 550 57 448 57 322S183 95 338 95H531ZM531 -40V10H86V-40H531Z" id="g117-75"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,49.062,0)"><path d="M723 650H473V615C541 611 564 591 570 556C575 526 580 488 580 417V310C580 143 528 53 409 53C301 53 247 140 247 290V508C247 602 257 608 330 615V650H29V615C103 608 113 602 113 508V272C113 155 140 81 196 36C244 -1 307 -15 373 -15C444 -15 512 10 558 58C614 118 630 202 630 308V417C630 488 634 525 639 556C644 591 669 612 723 615V650Z" id="g13-83"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="729" vert-adv-y="729"></glyph.data></g></svg>, and assemble a sample <svg height="12.0314pt" id="M29" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -8.7403 9.74492 12.0314" width="9.74492pt" 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="M442 495C434 557 427 602 423 639C405 645 348 665 284 665C142 665 55 579 55 469C55 373 127 319 229 267C304 227 348 190 348 131C348 67 309 25 248 25C152 25 93 138 73 202L38 190C45 130 58 46 68 21C81 15 100 7 128 -1C158 -10 193 -15 229 -15C375 -15 472 74 472 188C472 287 400 343 295 394C207 439 171 470 171 525C171 583 212 624 268 624C349 624 387 550 407 487L442 495Z" id="g13-81"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.565,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g></svg></td></tr><tr><td colspan="2">(3)  According to <svg height="12.0314pt" id="M30" style="vertical-align:-3.2911pt" version="1.1" viewbox="-0.0498162 -8.7403 9.74492 12.0314" width="9.74492pt" 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="M442 495C434 557 427 602 423 639C405 645 348 665 284 665C142 665 55 579 55 469C55 373 127 319 229 267C304 227 348 190 348 131C348 67 309 25 248 25C152 25 93 138 73 202L38 190C45 130 58 46 68 21C81 15 100 7 128 -1C158 -10 193 -15 229 -15C375 -15 472 74 472 188C472 287 400 343 295 394C207 439 171 470 171 525C171 583 212 624 268 624C349 624 387 550 407 487L442 495Z" id="g13-81"></path><glyph.data ascent="1024" descent="-360" horiz-adv-x="505" vert-adv-y="505"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.565,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g></svg>, compose the candidate hypothesis <svg height="12.5794pt" id="M31" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 9.82321 12.5794" width="9.82321pt" 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="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z" id="g113-105"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="516" vert-adv-y="516"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.643,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g></svg></td></tr><tr><td colspan="2">(4)  Calculate the degree of agreement <svg height="12.5794pt" id="M32" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 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Computational Intelligence and Neuroscience

psdc1

Pseudocode 1

Pseudocode 1: A Multiobjective Approach to Homography Estimation 