Approximately Nearest Neighborhood Image Search Using Unsupervised Hashing via Homogeneous Kernels

<div>Performance comparison using the Phow-RBF-<svg height="15.2296pt" id="M84" style="vertical-align:-3.6382pt" version="1.1" viewbox="-0.0498162 -11.5914 12.6404 15.2296" width="12.6404pt" 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="M565 434L556 448L482 423L322 189L287 373C280 410 261 448 236 448C207 448 161 415 110 338L131 317C160 355 181 374 193 374C204 374 208 366 217 330C230 279 247 185 259 116L50 -175C18 -223 29 -260 41 -278H51C97 -198 207 -33 270 57L313 -165C328 -235 349 -261 376 -261S445 -244 510 -150L487 -127C444 -178 423 -186 411 -186C402 -186 398 -177 387 -130C371 -62 349 39 332 135C390 217 524 392 565 434Z" id="g113-244"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.568,-5.741)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> kernel based on a <i>γ</i>-homogeneous kernel map with different values for <span class="nowrap"><svg height="9.49473pt" id="M85" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.21949 9.49473" width="6.21949pt" 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="M452 333C452 398 425 448 375 448C329 448 235 404 140 292H138L229 683C233 701 234 712 225 712C208 712 149 686 66 677L64 652H97C135 652 140 651 129 598L38 167C23 96 29 57 44 33C60 7 98 -12 132 -12C169 -12 232 3 290 41C383 102 452 223 452 333ZM365 316C365 199 308 87 239 49C221 39 200 35 183 35C137 35 99 70 112 163C116 191 123 215 129 233C190 316 290 392 330 392C348 392 365 372 365 316Z" id="g113-99"></path></g></svg>,</span> <span class="nowrap"><svg height="6.1673pt" id="M86" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 6.6501 6.1673" width="6.6501pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path></g></svg>,</span> and <span class="nowrap"><svg height="8.02022pt" id="M87" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path></g></svg>.</span></div>

Complexity

fig1

Figure 1

Figure 1: Approximately Nearest Neighborhood Image Search Using Unsupervised Hashing via Homogeneous Kernels 