Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td align="left">Various regions</td><td align="center"><span style="width: 21.5331ptpx;"><svg height="14.8173pt" id="M67" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 21.5331 14.8173" width="21.5331pt" 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="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z" id="g113-74"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="428" vert-adv-y="428"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.138,3.132)"><path d="M478 400C478 445 461 451 447 451C425 451 399 442 369 425C316 395 241 339 172 252H170L191 340C198 371 203 395 203 412C203 439 194 451 178 451C147 451 81 411 24 351L43 324C68 349 101 371 111 371C117 371 122 363 115 334L35 -4L42 -11C61 -4 87 3 117 9C130 72 144 130 158 181C241 296 342 379 383 379C398 379 404 370 384 285L330 60C302 -58 282 -164 282 -190S323 -257 354 -257L361 -243C357 -223 359 -177 382 -73L464 303C474 347 478 378 478 400Z" id="g50-229"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.871,3.132)"><path d="M478 400C478 445 461 451 447 451C425 451 399 442 369 425C316 395 241 339 172 252H170L191 340C198 371 203 395 203 412C203 439 194 451 178 451C147 451 81 411 24 351L43 324C68 349 101 371 111 371C117 371 122 363 115 334L35 -4L42 -11C61 -4 87 3 117 9C130 72 144 130 158 181C241 296 342 379 383 379C398 379 404 370 384 285L330 60C302 -58 282 -164 282 -190S323 -257 354 -257L361 -243C357 -223 359 -177 382 -73L464 303C474 347 478 378 478 400Z" id="g50-229"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="502" vert-adv-y="502"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,17.971,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g></svg></span></td><td align="center"><span style="width: 20.5009ptpx;"><svg height="14.2236pt" id="M68" style="vertical-align:-4.93527pt" version="1.1" viewbox="-0.0498162 -9.28833 20.5009 14.2236" width="20.5009pt" 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="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,3.419,0)"><path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z" id="g113-74"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="428" vert-adv-y="428"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.138,3.132)"><path d="M435 683C435 695 433 700 417 700C380 700 311 676 267 649C217 655 198 677 198 698C198 713 202 725 205 731L185 739C156 728 122 706 122 679C122 646 165 618 221 611C170 578 115 533 115 461C115 416 145 377 177 365C103 329 24 261 24 163C24 72 81 34 155 14C181 7 201 3 222 -1C284 -14 298 -34 298 -59C298 -97 254 -151 235 -171L262 -194C285 -179 378 -110 378 -28C378 14 343 58 273 70C248 74 219 80 190 89C140 104 109 134 109 190C109 259 165 325 225 350C251 343 285 340 318 340C334 340 376 381 376 403C376 416 372 420 355 420C323 420 284 410 258 403C221 409 194 444 194 490C194 540 236 586 274 608C317 608 364 613 388 623C408 631 435 653 435 683Z" id="g50-236"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="459" vert-adv-y="459"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.234,3.132)"><path d="M435 683C435 695 433 700 417 700C380 700 311 676 267 649C217 655 198 677 198 698C198 713 202 725 205 731L185 739C156 728 122 706 122 679C122 646 165 618 221 611C170 578 115 533 115 461C115 416 145 377 177 365C103 329 24 261 24 163C24 72 81 34 155 14C181 7 201 3 222 -1C284 -14 298 -34 298 -59C298 -97 254 -151 235 -171L262 -194C285 -179 378 -110 378 -28C378 14 343 58 273 70C248 74 219 80 190 89C140 104 109 134 109 190C109 259 165 325 225 350C251 343 285 340 318 340C334 340 376 381 376 403C376 416 372 420 355 420C323 420 284 410 258 403C221 409 194 444 194 490C194 540 236 586 274 608C317 608 364 613 388 623C408 631 435 653 435 683Z" id="g50-236"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="459" vert-adv-y="459"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,16.939,0)"><path d="M162 -163V703H101V-163H162Z" id="g113-9"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data></g></svg></span></td><td align="center"><span style="width: 10.095ptpx;"><svg height="8.68572pt" id="M69" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 10.095 8.68572" width="10.095pt" 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="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 229 46C205 55 202 71 212 126L293 553C300 588 306 600 317 606C330 613 356 617 390 617C547 617 644 537 644 379Z" id="g113-69"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="766" vert-adv-y="766"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td align="left">Edge</td><td align="center">Large</td><td align="center">Small</td><td align="center">Large</td></tr><tr><td align="left">Isolated noise</td><td align="center">Large</td><td align="center">Large</td><td align="center">Small</td></tr><tr><td align="left">Flat region</td><td align="center">Small</td><td align="center">Small</td><td align="center">Small</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The characteristic analysis of difference curvature.

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Patch Similarity Modulus and Difference Curvature Based Fourth-Order Partial Differential Equation for Image Denoising 