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GitHub - tbriand/reversibility_error: C implementation for computing the reversibility error of various interpolation methods.
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0 0 1-.052-1.086c0-1.331.282-2.499 1.132-3.368.397-.406.89-.717 1.474-.952 1.399-1.136 3.392-2.093 6.122-2.093 2.731 0 4.767.957 6.166 2.093.584.235 1.077.546 1.474.952.85.869 1.132 2.037 1.132 3.368 0 .368-.014.733-.052 1.086.23.462.477 1.088.644 1.517 1.258.364 2.233 1.721 2.605 2.656a.832.832 0 0 1 .053.22v2.869a.641.641 0 0 1-.078.256ZM12.172 11h-.344a4.323 4.323 0 0 1-.355.508C10.703 12.455 9.555 13 7.965 13c-1.725 0-2.989-.359-3.782-1.259a2.005 2.005 0 0 1-.085-.104L4 11.741v6.585c1.435.779 4.514 2.179 8 2.179 3.486 0 6.565-1.4 8-2.179v-6.585l-.098-.104s-.033.045-.085.104c-.793.9-2.057 1.259-3.782 1.259-1.59 0-2.738-.545-3.508-1.492a4.323 4.323 0 0 1-.355-.508h-.016.016Zm.641-2.935c.136 1.057.403 1.913.878 2.497.442.544 1.134.938 2.344.938 1.573 0 2.292-.337 2.657-.751.384-.435.558-1.15.558-2.361 0-1.14-.243-1.847-.705-2.319-.477-.488-1.319-.862-2.824-1.025-1.487-.161-2.192.138-2.533.529-.269.307-.437.808-.438 1.578v.021c0 .265.021.562.063.893Zm-1.626 0c.042-.331.063-.628.063-.894v-.02c-.001-.77-.169-1.271-.438-1.578-.341-.391-1.046-.69-2.533-.529-1.505.163-2.347.537-2.824 1.025-.462.472-.705 1.179-.705 2.319 0 1.211.175 1.926.558 2.361.365.414 1.084.751 2.657.751 1.21 0 1.902-.394 2.344-.938.475-.584.742-1.44.878-2.497Z"></path><path d="M14.5 14.25a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Zm-5 0a1 1 0 0 1 1 1v2a1 1 0 0 1-2 0v-2a1 1 0 0 1 1-1Z"></path> </svg> <div> <div class="color-fg-default h4">GitHub Copilot</div> Write better code with AI </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"security","context":"product","tag":"link","label":"security_link_product_navbar"}" href="https://github.com/features/security"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon 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href="https://github.com/features/actions"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-workflow color-fg-subtle mr-3"> <path d="M1 3a2 2 0 0 1 2-2h6.5a2 2 0 0 1 2 2v6.5a2 2 0 0 1-2 2H7v4.063C7 16.355 7.644 17 8.438 17H12.5v-2.5a2 2 0 0 1 2-2H21a2 2 0 0 1 2 2V21a2 2 0 0 1-2 2h-6.5a2 2 0 0 1-2-2v-2.5H8.437A2.939 2.939 0 0 1 5.5 15.562V11.5H3a2 2 0 0 1-2-2Zm2-.5a.5.5 0 0 0-.5.5v6.5a.5.5 0 0 0 .5.5h6.5a.5.5 0 0 0 .5-.5V3a.5.5 0 0 0-.5-.5ZM14.5 14a.5.5 0 0 0-.5.5V21a.5.5 0 0 0 .5.5H21a.5.5 0 0 0 .5-.5v-6.5a.5.5 0 0 0-.5-.5Z"></path> </svg> <div> <div class="color-fg-default h4">Actions</div> Automate any workflow </div> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description pb-lg-3" data-analytics-event="{"location":"navbar","action":"codespaces","context":"product","tag":"link","label":"codespaces_link_product_navbar"}" href="https://github.com/features/codespaces"> <svg aria-hidden="true" height="24" viewBox="0 0 24 24" version="1.1" width="24" data-view-component="true" class="octicon octicon-codespaces color-fg-subtle mr-3"> <path d="M3.5 3.75C3.5 2.784 4.284 2 5.25 2h13.5c.966 0 1.75.784 1.75 1.75v7.5A1.75 1.75 0 0 1 18.75 13H5.25a1.75 1.75 0 0 1-1.75-1.75Zm-2 12c0-.966.784-1.75 1.75-1.75h17.5c.966 0 1.75.784 1.75 1.75v4a1.75 1.75 0 0 1-1.75 1.75H3.25a1.75 1.75 0 0 1-1.75-1.75ZM5.25 3.5a.25.25 0 0 0-.25.25v7.5c0 .138.112.25.25.25h13.5a.25.25 0 0 0 .25-.25v-7.5a.25.25 0 0 0-.25-.25Zm-2 12a.25.25 0 0 0-.25.25v4c0 .138.112.25.25.25h17.5a.25.25 0 0 0 .25-.25v-4a.25.25 0 0 0-.25-.25Z"></path><path d="M10 17.75a.75.75 0 0 1 .75-.75h6.5a.75.75 0 0 1 0 1.5h-6.5a.75.75 0 0 1-.75-.75Zm-4 0a.75.75 0 0 1 .75-.75h.5a.75.75 0 0 1 0 1.5h-.5a.75.75 0 0 1-.75-.75Z"></path> 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data-view-component="true" class="octicon octicon-code-square color-fg-subtle mr-3"> <path d="M10.3 8.24a.75.75 0 0 1-.04 1.06L7.352 12l2.908 2.7a.75.75 0 1 1-1.02 1.1l-3.5-3.25a.75.75 0 0 1 0-1.1l3.5-3.25a.75.75 0 0 1 1.06.04Zm3.44 1.06a.75.75 0 1 1 1.02-1.1l3.5 3.25a.75.75 0 0 1 0 1.1l-3.5 3.25a.75.75 0 1 1-1.02-1.1l2.908-2.7-2.908-2.7Z"></path><path d="M2 3.75C2 2.784 2.784 2 3.75 2h16.5c.966 0 1.75.784 1.75 1.75v16.5A1.75 1.75 0 0 1 20.25 22H3.75A1.75 1.75 0 0 1 2 20.25Zm1.75-.25a.25.25 0 0 0-.25.25v16.5c0 .138.112.25.25.25h16.5a.25.25 0 0 0 .25-.25V3.75a.25.25 0 0 0-.25-.25Z"></path> </svg> <div> <div class="color-fg-default h4">Code Search</div> Find more, search less </div> </a></li> </ul> </div> </div> <div class="HeaderMenu-column px-lg-4"> <div class="border-bottom pb-3 pb-lg-0 border-lg-bottom-0 border-bottom-0"> <span class="d-block h4 color-fg-default my-1" id="product-explore-heading">Explore</span> <ul class="list-style-none f5" aria-labelledby="product-explore-heading"> 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0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 2Zm6.854-1h4.146a.25.25 0 0 1 .25.25v4.146a.25.25 0 0 1-.427.177L13.03 4.03 9.28 7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary Link--external" target="_blank" data-analytics-event="{"location":"navbar","action":"github_skills","context":"product","tag":"link","label":"github_skills_link_product_navbar"}" href="https://skills.github.com"> GitHub Skills <svg aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-link-external HeaderMenu-external-icon color-fg-subtle"> <path d="M3.75 2h3.5a.75.75 0 0 1 0 1.5h-3.5a.25.25 0 0 0-.25.25v8.5c0 .138.112.25.25.25h8.5a.25.25 0 0 0 .25-.25v-3.5a.75.75 0 0 1 1.5 0v3.5A1.75 1.75 0 0 1 12.25 14h-8.5A1.75 1.75 0 0 1 2 12.25v-8.5C2 2.784 2.784 2 3.75 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7.78a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042l3.75-3.75-1.543-1.543A.25.25 0 0 1 10.604 1Z"></path> </svg> </a></li> </ul> </div> </div> </div> </li> <li class="HeaderMenu-item position-relative flex-wrap flex-justify-between flex-items-center d-block d-lg-flex flex-lg-nowrap flex-lg-items-center js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Solutions <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 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height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4"> <div class="HeaderMenu-column"> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary d-flex flex-items-center Link--has-description" data-analytics-event="{"location":"navbar","action":"github_sponsors","context":"open_source","tag":"link","label":"github_sponsors_link_open_source_navbar"}" href="/sponsors"> <div> <div class="color-fg-default h4">GitHub Sponsors</div> 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js-details-container js-header-menu-item"> <button type="button" class="HeaderMenu-link border-0 width-full width-lg-auto px-0 px-lg-2 py-lg-2 no-wrap d-flex flex-items-center flex-justify-between js-details-target" aria-expanded="false"> Enterprise <svg opacity="0.5" aria-hidden="true" height="16" viewBox="0 0 16 16" version="1.1" width="16" data-view-component="true" class="octicon octicon-chevron-down HeaderMenu-icon ml-1"> <path d="M12.78 5.22a.749.749 0 0 1 0 1.06l-4.25 4.25a.749.749 0 0 1-1.06 0L3.22 6.28a.749.749 0 1 1 1.06-1.06L8 8.939l3.72-3.719a.749.749 0 0 1 1.06 0Z"></path> </svg> </button> <div class="HeaderMenu-dropdown dropdown-menu rounded m-0 p-0 pt-2 pt-lg-4 position-relative position-lg-absolute left-0 left-lg-n3 pb-2 pb-lg-4 px-lg-4"> <div class="HeaderMenu-column"> <div class="border-bottom pb-3 pb-lg-0 pb-lg-3 mb-3 mb-lg-0 mb-lg-3"> <ul class="list-style-none f5" > <li> <a class="HeaderMenu-dropdown-link d-block no-underline position-relative py-2 Link--secondary 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class=\"heading-element\" dir=\"auto\"\u003eReversibility Error of Image Interpolation Methods: Definition and Improvements\u003c/h1\u003e\u003ca id=\"user-content-reversibility-error-of-image-interpolation-methods-definition-and-improvements\" class=\"anchor\" aria-label=\"Permalink: Reversibility Error of Image Interpolation Methods: Definition and Improvements\" href=\"#reversibility-error-of-image-interpolation-methods-definition-and-improvements\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eSummary\u003c/h2\u003e\u003ca id=\"user-content-summary\" class=\"anchor\" aria-label=\"Permalink: Summary\" href=\"#summary\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis repository contains programs for the evaluation of the reversibility error\nof interpolation methods.\nIt is part of an \u003ca href=\"https://doi.org/10.5201/ipol.2019.277\" rel=\"nofollow\"\u003eIPOL publication\u003c/a\u003e\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eAuthors\u003c/h2\u003e\u003ca id=\"user-content-authors\" class=\"anchor\" aria-label=\"Permalink: Authors\" href=\"#authors\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eThibaud Briand \u003ca href=\"mailto:briand.thibaud@gmail.com\"\u003ebriand.thibaud@gmail.com\u003c/a\u003e\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eLaboratoire d'Informatique Gaspard Monge (LIGM)/ Ecole des Ponts ParisTech\nCentre de mathématiques et de leurs applications (CMLA)/ ENS Paris-Saclay\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eVersions\u003c/h2\u003e\u003ca id=\"user-content-versions\" class=\"anchor\" aria-label=\"Permalink: Versions\" href=\"#versions\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eVersion 1.0, released on 2019-10-16 : Original version.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eVersion 1.01, released on 2020-10-12 : Fix requirements for the IPOL demo.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eLicense\u003c/h2\u003e\u003ca id=\"user-content-license\" class=\"anchor\" aria-label=\"Permalink: License\" href=\"#license\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThis program is free software: you can redistribute it and/or modify it\nunder the terms of the GNU General Public License as published by\nthe Free Software Foundation, either version 2 of the License, or\n(at your option) any later version.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eYou should have received a copy of the GNU General Public License\nalong with this program. If not, see \u003ca href=\"http://www.gnu.org/licenses/\" rel=\"nofollow\"\u003ehttp://www.gnu.org/licenses/\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eCopyright (C) 2018-2019, Thibaud Briand \u003ca href=\"mailto:briand.thibaud@gmail.com\"\u003ebriand.thibaud@gmail.com\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eAll rights reserved.\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eBuild\u003c/h2\u003e\u003ca id=\"user-content-build\" class=\"anchor\" aria-label=\"Permalink: Build\" href=\"#build\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eRequired environment: Any unix-like system with a standard compilation\nenvironment (make and C compiler) and \u003ca href=\"https://cmake.org/\" rel=\"nofollow\"\u003eCmake\u003c/a\u003e.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eRequired libraries:\n\u003ca href=\"http://libpng.org/pub/png/libpng.html\" rel=\"nofollow\"\u003elibpng\u003c/a\u003e,\n\u003ca href=\"http://ijg.org/\" rel=\"nofollow\"\u003elipjpeg\u003c/a\u003e,\n\u003ca href=\"http://simplesystems.org/libtiff/\" rel=\"nofollow\"\u003elibtiff\u003c/a\u003e\n\u003ca href=\"http://www.fftw.org/\" rel=\"nofollow\"\u003elibfftw3\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eOptional libraries:\n\u003ca href=\"https://www.openmp.org/\" rel=\"nofollow\"\u003elibopenmp\u003c/a\u003e\n\u003ca href=\"https://www.gnu.org/software/gsl/\" rel=\"nofollow\"\u003eGSL\u003c/a\u003e\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eBuild instructions:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" mkdir build\n cd build\n cmake -DCMAKE_BUILD_TYPE=Release ..\n make\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e mkdir build\n cd build\n cmake -DCMAKE_BUILD_TYPE=Release ..\n make\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eIt produces programs \"create_burst\", \"crop\", \"interpolation\", \"reversibility_error\" and \"spectrum_clipping\".\u003c/p\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage of create_burst\u003c/h2\u003e\u003ca id=\"user-content-usage-of-create_burst\" class=\"anchor\" aria-label=\"Permalink: Usage of create_burst\" href=\"#usage-of-create_burst\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe program reads an input image, a number of images, optionnally takes some parameters and\nproduces a burst of images.\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"\u0026lt;Usage\u0026gt;: ./create_burst input base number [OPTIONS]\n\n Output images are written as base_%i.tiff\n Output cropped images are written as base_crop_%i.tiff\n Homographies are written as base_%i.hom\n Homographies after crop are written as base_crop_%i.hom\n The first image of the generated sequence is the reference (identity)\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e\u0026lt;Usage\u0026gt;: ./create_burst input base number [OPTIONS]\n\n Output images are written as base_%i.tiff\n Output cropped images are written as base_crop_%i.tiff\n Homographies are written as base_%i.hom\n Homographies after crop are written as base_crop_%i.hom\n The first image of the generated sequence is the reference (identity)\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe optional parameters are:\n-c, Specify the crop size (by default 0)\n-L, Specify the displacement of the corners (by default 3)\n-i, Specify the interpolation method (by default p+s-spline11-spline1)\n-b, Specify the boundary condition between hsym, wsym, per and constant (by default hsym)\n-t, Specify the type of transformation (2 translation, 3 euclidean, 6 affinity, 8 homography (default))\n-z, Specify the down-sampling factor (by default 1)\n-n, Specify the standard deviation of the noise (by default 0)\n-s, Specify the seed of the random generator (by default 0)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExecution examples:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eBurst of 10 + 1 images:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./create_burst input.png base 11\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eBurst of 100 + 1 images with a crop of 20 pixels using the zoomed bicubic interpolation method:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./create_burst input.png base 101 -c 20 -i bic-z2\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage of crop\u003c/h2\u003e\u003ca id=\"user-content-usage-of-crop\" class=\"anchor\" aria-label=\"Permalink: Usage of crop\" href=\"#usage-of-crop\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe program reads an input image and the four bounds of the image domain,\nand performs the crop of the image.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e: ./crop x0 y0 xf yf in out\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExecution examples:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003eCrop in a band of 20 pixels:\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"./crop 10 10 -10 -10 input.png output.png\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e./crop 10 10 -10 -10 input.png output.png\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003col start=\"2\" dir=\"auto\"\u003e\n\u003cli\u003eRemove the last column of an image:\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"./crop 0 0 -1 0 input.png output.png\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e./crop 0 0 -1 0 input.png output.png\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage of interpolation\u003c/h2\u003e\u003ca id=\"user-content-usage-of-interpolation\" class=\"anchor\" aria-label=\"Permalink: Usage of interpolation\" href=\"#usage-of-interpolation\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe program reads an input image, an homography, optionnally takes some parameters\nand produces the corresponding transformed image.\nThis may use Algorithm 3 or Algorithm 4.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e: ./interpolation input output \"h11 h12 h13 h21 h22 h23 h31 h32 h33\" [OPTIONS]\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe optional parameters are:\n-i, Specify the interpolation method (by default p+s-spline11-spline1)\n-b, Specify the boundary condition between hsym, wsym, per and constant (by default hsym)\n-t, Set to 1 to apply the inverse transform (by default 0)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExecution examples:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eTranslation of (1.5,-2.3):\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./interpolation input.png output.tiff \"1 0 1.5 0 1 -2.3 0 0 1\"\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eApply the inverse of an homography using bicubic interpolation with periodic extension:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./interpolation input.png output.tiff \"h11 h12 h13 h21 h22 h23 h31 h32 h33\" -i bic -b periodic -t 1\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage of reversibility_error\u003c/h2\u003e\u003ca id=\"user-content-usage-of-reversibility_error\" class=\"anchor\" aria-label=\"Permalink: Usage of reversibility_error\" href=\"#usage-of-reversibility_error\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe program reads two input images and computes the reversibility error (or clipped reversibility error).\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e: ./reversibility_error input1 input2 clipped -r ratio\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" Set clipped to 1 to compute the clipped reversibility error\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e Set clipped to 1 to compute the clipped reversibility error\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe optional parameter is:\n-r, Specify the ratio of clipped high-frequencies (by default 0.050000)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExecution examples:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eReversibility error:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./reversibility_error input1.tiff input2.tiff 0\u003c/p\u003e\n\u003c/li\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eClipped reversibility error with ratio 10%:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./reversibility_error input1.tiff input2.tiff 1 -r 0.1\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage of spectrum_clipping\u003c/h2\u003e\u003ca id=\"user-content-usage-of-spectrum_clipping\" class=\"anchor\" aria-label=\"Permalink: Usage of spectrum_clipping\" href=\"#usage-of-spectrum_clipping\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe program reads an input image and its spectrum clipped version.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e: ./spectrum_clipping input1 input2 [-r ratio]\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eThe optional parameter is:\n-r, Specify the ratio of clipped high-frequencies (by default 0.050000)\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExecution examples:\u003c/p\u003e\n\u003col dir=\"auto\"\u003e\n\u003cli\u003e\n\u003cp dir=\"auto\"\u003eSpectrum clipping with ratio 10%:\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e./spectrum_clipping input.png output.tiff -r 0.1\u003c/p\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eUsage of the demo script run.sh\u003c/h2\u003e\u003ca id=\"user-content-usage-of-the-demo-script-runsh\" class=\"anchor\" aria-label=\"Permalink: Usage of the demo script run.sh\" href=\"#usage-of-the-demo-script-runsh\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eThe script reads an image, the displacement of the image four corners,\nthe interpolation method and the reversibility error parameters.\nIt computes the transformed image, the reversibility errors, the difference images\nand its DFT.\u003c/p\u003e\n\u003cp dir=\"auto\"\u003e: bin=path_to_demo_directory ./run.sh in baseout hx1 hy1 hx2 hy2 hx3 hy3 hx4 hy4 crop interp boundary ratio\u003c/p\u003e\n\u003cp dir=\"auto\"\u003eExecution example:\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\" bin=demo/ demo/run.sh input.png baseout 1 1 -1 -1 0 0 1 1 20 spline11 hsym 0.01\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003e bin=demo/ demo/run.sh input.png baseout 1 1 -1 -1 0 0 1 1 20 spline11 hsym 0.01\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cp dir=\"auto\"\u003eNote that the execution of the script requires the programs \"crop\", \"interpolation\" and\n\"reversibility_error\". The user should add these programs to the Path. For instance\nthis can be done using the command\u003c/p\u003e\n\u003cdiv class=\"snippet-clipboard-content notranslate position-relative overflow-auto\" data-snippet-clipboard-copy-content=\"PATH=path_to_build_directory:$PATH\"\u003e\u003cpre class=\"notranslate\"\u003e\u003ccode\u003ePATH=path_to_build_directory:$PATH\n\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\n\u003cdiv class=\"markdown-heading\" dir=\"auto\"\u003e\u003ch2 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\"\u003eList of files\u003c/h2\u003e\u003ca id=\"user-content-list-of-files\" class=\"anchor\" aria-label=\"Permalink: List of files\" href=\"#list-of-files\"\u003e\u003csvg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"\u003e\u003cpath d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"\u003e\u003c/path\u003e\u003c/svg\u003e\u003c/a\u003e\u003c/div\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003eCMakeList.txt : CMake file for the compilation\u003c/li\u003e\n\u003cli\u003eFindGSL.cmake\t\t : CMAke file for finding GNU scientific library GSL\u003c/li\u003e\n\u003cli\u003eLICENSE\t\t : License file\u003c/li\u003e\n\u003cli\u003eREADME.txt : This file\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eIn the data/ directory:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003erubberwhale_gray.png : Test image (grayscale)\u003c/li\u003e\n\u003cli\u003ebaboon.png\t\t : Test image (color)\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eIn the demo/ directory:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003edifference_and_fft.py : Program to display the difference image and its spectrum in the demo\u003c/li\u003e\n\u003cli\u003ehom4p.py : Program to compute a homography from four corresponding points\u003c/li\u003e\n\u003cli\u003erequirements.txt : Package used by the demo\u003c/li\u003e\n\u003cli\u003erun.sh : Main script of the demo. This corresponds to Algorithm 2 with Ntransf=1\u003c/li\u003e\n\u003cli\u003etranslate_homography.py : Program to translate a homography\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eIn the src/ directory:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003ebicubic.[hc] : Functions to perform bicubic interpolation\u003c/li\u003e\n\u003cli\u003ecompute_core.h\t : Utility functions for the crop and the rmse\u003c/li\u003e\n\u003cli\u003efft_core.[hc] : Functions related to the Fourier computations\u003c/li\u003e\n\u003cli\u003ehomography_core.[hc]\t : Functions related to homographies (contains Algorithm 1)\u003c/li\u003e\n\u003cli\u003einterpolation_core.[hc] : Functions to perform a geometric transformation using interpolation (contains Algorithm 3 and Algorithm 4)\u003c/li\u003e\n\u003cli\u003emain_create_burst.c : Main program for creating a burst from an image (in particular it generates random homographies)\u003c/li\u003e\n\u003cli\u003emain_crop.c : Main program for cropping an image\u003c/li\u003e\n\u003cli\u003emain_interpolation.c : Main program for input/ouput (Algorithm 3 and Algorithm 4)\u003c/li\u003e\n\u003cli\u003emain_reversibility_error.c : Main program for computing the reversibility error\u003c/li\u003e\n\u003cli\u003emain_spectrum_clipping.c : Main program for computing the spectrum clipping\u003c/li\u003e\n\u003cli\u003eperiodic_plus_smooth.[hc] : Functions to compute the periodic plus smooth decomposition of an image\u003c/li\u003e\n\u003cli\u003etpi.[hc] : Functions to perform trigonometric polynomial interpolation\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp dir=\"auto\"\u003eAdditional files are provided in the external/ directory:\u003c/p\u003e\n\u003cul dir=\"auto\"\u003e\n\u003cli\u003ecmphomod.h : Functions to compute an homography from four correspondences\u003c/li\u003e\n\u003cli\u003eiio.[hc] : Functions for opening images in any format\u003c/li\u003e\n\u003cli\u003erandom.h : Functions to generate random numbers\u003c/li\u003e\n\u003cli\u003exmtime.h : Clock with millisecond precision\u003c/li\u003e\n\u003cli\u003ebspline : Functions to perform B-spline interpolation\u003c/li\u003e\n\u003cli\u003enfft-3.5.0 : NFFT3 library\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/article\u003e","loaded":true,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":[{"level":1,"text":"Reversibility Error of Image Interpolation Methods: Definition and Improvements","anchor":"reversibility-error-of-image-interpolation-methods-definition-and-improvements","htmlText":"Reversibility Error of Image Interpolation Methods: Definition and Improvements"},{"level":2,"text":"Summary","anchor":"summary","htmlText":"Summary"},{"level":2,"text":"Authors","anchor":"authors","htmlText":"Authors"},{"level":2,"text":"Versions","anchor":"versions","htmlText":"Versions"},{"level":2,"text":"License","anchor":"license","htmlText":"License"},{"level":2,"text":"Build","anchor":"build","htmlText":"Build"},{"level":2,"text":"Usage of create_burst","anchor":"usage-of-create_burst","htmlText":"Usage of create_burst"},{"level":2,"text":"Usage of crop","anchor":"usage-of-crop","htmlText":"Usage of crop"},{"level":2,"text":"Usage of interpolation","anchor":"usage-of-interpolation","htmlText":"Usage of interpolation"},{"level":2,"text":"Usage of reversibility_error","anchor":"usage-of-reversibility_error","htmlText":"Usage of reversibility_error"},{"level":2,"text":"Usage of spectrum_clipping","anchor":"usage-of-spectrum_clipping","htmlText":"Usage of spectrum_clipping"},{"level":2,"text":"Usage of the demo script run.sh","anchor":"usage-of-the-demo-script-runsh","htmlText":"Usage of the demo script run.sh"},{"level":2,"text":"List of files","anchor":"list-of-files","htmlText":"List of files"}],"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Ftbriand%2Freversibility_error"}},{"displayName":"LICENSE","repoName":"reversibility_error","refName":"master","path":"LICENSE","preferredFileType":"license","tabName":"GPL-2.0","richText":null,"loaded":false,"timedOut":false,"errorMessage":null,"headerInfo":{"toc":null,"siteNavLoginPath":"/login?return_to=https%3A%2F%2Fgithub.com%2Ftbriand%2Freversibility_error"}}],"overviewFilesProcessingTime":0}},"appPayload":{"helpUrl":"https://docs.github.com","findFileWorkerPath":"/assets-cdn/worker/find-file-worker-9f8a877aa99f.js","findInFileWorkerPath":"/assets-cdn/worker/find-in-file-worker-96e76d5fdb2c.js","githubDevUrl":null,"enabled_features":{"copilot_workspace":null,"code_nav_ui_events":false,"overview_shared_code_dropdown_button":false,"react_blob_overlay":false,"copilot_conversational_ux_embedding_update":false,"copilot_smell_icebreaker_ux":true,"accessible_code_button":true}}}}</script> <div 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1.5h-8.5a.75.75 0 0 1 0-1.5Zm0 5h8.5a.75.75 0 0 1 0 1.5h-8.5a.75.75 0 0 1 0-1.5ZM2 14a1 1 0 1 1 0-2 1 1 0 0 1 0 2Zm1-6a1 1 0 1 1-2 0 1 1 0 0 1 2 0ZM2 4a1 1 0 1 1 0-2 1 1 0 0 1 0 2Z"></path></svg></button></div><div class="Box-sc-g0xbh4-0 QkQOb js-snippet-clipboard-copy-unpositioned undefined" data-hpc="true"><article class="markdown-body entry-content container-lg" itemprop="text"><div class="markdown-heading" dir="auto"><h1 tabindex="-1" class="heading-element" dir="auto">Reversibility Error of Image Interpolation Methods: Definition and Improvements</h1><a id="user-content-reversibility-error-of-image-interpolation-methods-definition-and-improvements" class="anchor" aria-label="Permalink: Reversibility Error of Image Interpolation Methods: Definition and Improvements" href="#reversibility-error-of-image-interpolation-methods-definition-and-improvements"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Summary</h2><a id="user-content-summary" class="anchor" aria-label="Permalink: Summary" href="#summary"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This repository contains programs for the evaluation of the reversibility error of interpolation methods. It is part of an <a href="https://doi.org/10.5201/ipol.2019.277" rel="nofollow">IPOL publication</a></p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Authors</h2><a id="user-content-authors" class="anchor" aria-label="Permalink: Authors" href="#authors"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>Thibaud Briand <a href="mailto:briand.thibaud@gmail.com">briand.thibaud@gmail.com</a></li> </ul> <p dir="auto">Laboratoire d'Informatique Gaspard Monge (LIGM)/ Ecole des Ponts ParisTech Centre de mathématiques et de leurs applications (CMLA)/ ENS Paris-Saclay</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Versions</h2><a id="user-content-versions" class="anchor" aria-label="Permalink: Versions" href="#versions"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Version 1.0, released on 2019-10-16 : Original version.</p> <p dir="auto">Version 1.01, released on 2020-10-12 : Fix requirements for the IPOL demo.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">License</h2><a id="user-content-license" class="anchor" aria-label="Permalink: License" href="#license"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 2 of the License, or (at your option) any later version.</p> <p dir="auto">You should have received a copy of the GNU General Public License along with this program. If not, see <a href="http://www.gnu.org/licenses/" rel="nofollow">http://www.gnu.org/licenses/</a>.</p> <p dir="auto">Copyright (C) 2018-2019, Thibaud Briand <a href="mailto:briand.thibaud@gmail.com">briand.thibaud@gmail.com</a></p> <p dir="auto">All rights reserved.</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Build</h2><a id="user-content-build" class="anchor" aria-label="Permalink: Build" href="#build"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">Required environment: Any unix-like system with a standard compilation environment (make and C compiler) and <a href="https://cmake.org/" rel="nofollow">Cmake</a>.</p> <p dir="auto">Required libraries: <a href="http://libpng.org/pub/png/libpng.html" rel="nofollow">libpng</a>, <a href="http://ijg.org/" rel="nofollow">lipjpeg</a>, <a href="http://simplesystems.org/libtiff/" rel="nofollow">libtiff</a> <a href="http://www.fftw.org/" rel="nofollow">libfftw3</a></p> <p dir="auto">Optional libraries: <a href="https://www.openmp.org/" rel="nofollow">libopenmp</a> <a href="https://www.gnu.org/software/gsl/" rel="nofollow">GSL</a></p> <p dir="auto">Build instructions:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" mkdir build cd build cmake -DCMAKE_BUILD_TYPE=Release .. make"><pre class="notranslate"><code> mkdir build cd build cmake -DCMAKE_BUILD_TYPE=Release .. make </code></pre></div> <p dir="auto">It produces programs "create_burst", "crop", "interpolation", "reversibility_error" and "spectrum_clipping".</p> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage of create_burst</h2><a id="user-content-usage-of-create_burst" class="anchor" aria-label="Permalink: Usage of create_burst" href="#usage-of-create_burst"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The program reads an input image, a number of images, optionnally takes some parameters and produces a burst of images.</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="<Usage>: ./create_burst input base number [OPTIONS] Output images are written as base_%i.tiff Output cropped images are written as base_crop_%i.tiff Homographies are written as base_%i.hom Homographies after crop are written as base_crop_%i.hom The first image of the generated sequence is the reference (identity)"><pre class="notranslate"><code><Usage>: ./create_burst input base number [OPTIONS] Output images are written as base_%i.tiff Output cropped images are written as base_crop_%i.tiff Homographies are written as base_%i.hom Homographies after crop are written as base_crop_%i.hom The first image of the generated sequence is the reference (identity) </code></pre></div> <p dir="auto">The optional parameters are: -c, Specify the crop size (by default 0) -L, Specify the displacement of the corners (by default 3) -i, Specify the interpolation method (by default p+s-spline11-spline1) -b, Specify the boundary condition between hsym, wsym, per and constant (by default hsym) -t, Specify the type of transformation (2 translation, 3 euclidean, 6 affinity, 8 homography (default)) -z, Specify the down-sampling factor (by default 1) -n, Specify the standard deviation of the noise (by default 0) -s, Specify the seed of the random generator (by default 0)</p> <p dir="auto">Execution examples:</p> <ol dir="auto"> <li> <p dir="auto">Burst of 10 + 1 images:</p> <p dir="auto">./create_burst input.png base 11</p> </li> <li> <p dir="auto">Burst of 100 + 1 images with a crop of 20 pixels using the zoomed bicubic interpolation method:</p> <p dir="auto">./create_burst input.png base 101 -c 20 -i bic-z2</p> </li> </ol> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage of crop</h2><a id="user-content-usage-of-crop" class="anchor" aria-label="Permalink: Usage of crop" href="#usage-of-crop"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The program reads an input image and the four bounds of the image domain, and performs the crop of the image.</p> <p dir="auto">: ./crop x0 y0 xf yf in out</p> <p dir="auto">Execution examples:</p> <ol dir="auto"> <li>Crop in a band of 20 pixels:</li> </ol> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="./crop 10 10 -10 -10 input.png output.png"><pre class="notranslate"><code>./crop 10 10 -10 -10 input.png output.png </code></pre></div> <ol start="2" dir="auto"> <li>Remove the last column of an image:</li> </ol> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="./crop 0 0 -1 0 input.png output.png"><pre class="notranslate"><code>./crop 0 0 -1 0 input.png output.png </code></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage of interpolation</h2><a id="user-content-usage-of-interpolation" class="anchor" aria-label="Permalink: Usage of interpolation" href="#usage-of-interpolation"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The program reads an input image, an homography, optionnally takes some parameters and produces the corresponding transformed image. This may use Algorithm 3 or Algorithm 4.</p> <p dir="auto">: ./interpolation input output "h11 h12 h13 h21 h22 h23 h31 h32 h33" [OPTIONS]</p> <p dir="auto">The optional parameters are: -i, Specify the interpolation method (by default p+s-spline11-spline1) -b, Specify the boundary condition between hsym, wsym, per and constant (by default hsym) -t, Set to 1 to apply the inverse transform (by default 0)</p> <p dir="auto">Execution examples:</p> <ol dir="auto"> <li> <p dir="auto">Translation of (1.5,-2.3):</p> <p dir="auto">./interpolation input.png output.tiff "1 0 1.5 0 1 -2.3 0 0 1"</p> </li> <li> <p dir="auto">Apply the inverse of an homography using bicubic interpolation with periodic extension:</p> <p dir="auto">./interpolation input.png output.tiff "h11 h12 h13 h21 h22 h23 h31 h32 h33" -i bic -b periodic -t 1</p> </li> </ol> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage of reversibility_error</h2><a id="user-content-usage-of-reversibility_error" class="anchor" aria-label="Permalink: Usage of reversibility_error" href="#usage-of-reversibility_error"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The program reads two input images and computes the reversibility error (or clipped reversibility error).</p> <p dir="auto">: ./reversibility_error input1 input2 clipped -r ratio</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" Set clipped to 1 to compute the clipped reversibility error"><pre class="notranslate"><code> Set clipped to 1 to compute the clipped reversibility error </code></pre></div> <p dir="auto">The optional parameter is: -r, Specify the ratio of clipped high-frequencies (by default 0.050000)</p> <p dir="auto">Execution examples:</p> <ol dir="auto"> <li> <p dir="auto">Reversibility error:</p> <p dir="auto">./reversibility_error input1.tiff input2.tiff 0</p> </li> <li> <p dir="auto">Clipped reversibility error with ratio 10%:</p> <p dir="auto">./reversibility_error input1.tiff input2.tiff 1 -r 0.1</p> </li> </ol> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage of spectrum_clipping</h2><a id="user-content-usage-of-spectrum_clipping" class="anchor" aria-label="Permalink: Usage of spectrum_clipping" href="#usage-of-spectrum_clipping"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The program reads an input image and its spectrum clipped version.</p> <p dir="auto">: ./spectrum_clipping input1 input2 [-r ratio]</p> <p dir="auto">The optional parameter is: -r, Specify the ratio of clipped high-frequencies (by default 0.050000)</p> <p dir="auto">Execution examples:</p> <ol dir="auto"> <li> <p dir="auto">Spectrum clipping with ratio 10%:</p> <p dir="auto">./spectrum_clipping input.png output.tiff -r 0.1</p> </li> </ol> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">Usage of the demo script run.sh</h2><a id="user-content-usage-of-the-demo-script-runsh" class="anchor" aria-label="Permalink: Usage of the demo script run.sh" href="#usage-of-the-demo-script-runsh"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <p dir="auto">The script reads an image, the displacement of the image four corners, the interpolation method and the reversibility error parameters. It computes the transformed image, the reversibility errors, the difference images and its DFT.</p> <p dir="auto">: bin=path_to_demo_directory ./run.sh in baseout hx1 hy1 hx2 hy2 hx3 hy3 hx4 hy4 crop interp boundary ratio</p> <p dir="auto">Execution example:</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content=" bin=demo/ demo/run.sh input.png baseout 1 1 -1 -1 0 0 1 1 20 spline11 hsym 0.01"><pre class="notranslate"><code> bin=demo/ demo/run.sh input.png baseout 1 1 -1 -1 0 0 1 1 20 spline11 hsym 0.01 </code></pre></div> <p dir="auto">Note that the execution of the script requires the programs "crop", "interpolation" and "reversibility_error". The user should add these programs to the Path. For instance this can be done using the command</p> <div class="snippet-clipboard-content notranslate position-relative overflow-auto" data-snippet-clipboard-copy-content="PATH=path_to_build_directory:$PATH"><pre class="notranslate"><code>PATH=path_to_build_directory:$PATH </code></pre></div> <div class="markdown-heading" dir="auto"><h2 tabindex="-1" class="heading-element" dir="auto">List of files</h2><a id="user-content-list-of-files" class="anchor" aria-label="Permalink: List of files" href="#list-of-files"><svg class="octicon octicon-link" viewBox="0 0 16 16" version="1.1" width="16" height="16" aria-hidden="true"><path d="m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z"></path></svg></a></div> <ul dir="auto"> <li>CMakeList.txt : CMake file for the compilation</li> <li>FindGSL.cmake : CMAke file for finding GNU scientific library GSL</li> <li>LICENSE : License file</li> <li>README.txt : This file</li> </ul> <p dir="auto">In the data/ directory:</p> <ul dir="auto"> <li>rubberwhale_gray.png : Test image (grayscale)</li> <li>baboon.png : Test image (color)</li> </ul> <p dir="auto">In the demo/ directory:</p> <ul dir="auto"> <li>difference_and_fft.py : Program to display the difference image and its spectrum in the demo</li> <li>hom4p.py : Program to compute a homography from four corresponding points</li> <li>requirements.txt : Package used by the demo</li> <li>run.sh : Main script of the demo. This corresponds to Algorithm 2 with Ntransf=1</li> <li>translate_homography.py : Program to translate a homography</li> </ul> <p dir="auto">In the src/ directory:</p> <ul dir="auto"> <li>bicubic.[hc] : Functions to perform bicubic interpolation</li> <li>compute_core.h : Utility functions for the crop and the rmse</li> <li>fft_core.[hc] : Functions related to the Fourier computations</li> <li>homography_core.[hc] : Functions related to homographies (contains Algorithm 1)</li> <li>interpolation_core.[hc] : Functions to perform a geometric transformation using interpolation (contains Algorithm 3 and Algorithm 4)</li> <li>main_create_burst.c : Main program for creating a burst from an image (in particular it generates random homographies)</li> <li>main_crop.c : Main program for cropping an image</li> <li>main_interpolation.c : Main program for input/ouput (Algorithm 3 and Algorithm 4)</li> <li>main_reversibility_error.c : Main program for computing the reversibility error</li> <li>main_spectrum_clipping.c : Main program for computing the spectrum clipping</li> <li>periodic_plus_smooth.[hc] : Functions to compute the periodic plus smooth decomposition of an image</li> <li>tpi.[hc] : Functions to perform trigonometric polynomial interpolation</li> </ul> <p dir="auto">Additional files are provided in the external/ directory:</p> <ul dir="auto"> <li>cmphomod.h : Functions to compute an homography from four correspondences</li> <li>iio.[hc] : Functions for opening images in any format</li> <li>random.h : Functions to generate random numbers</li> <li>xmtime.h : Clock with millisecond precision</li> <li>bspline : Functions to perform B-spline interpolation</li> <li>nfft-3.5.0 : NFFT3 library</li> </ul> </article></div></div></div></div></div> <!-- --> <!-- --> <script type="application/json" id="__PRIMER_DATA_:R0:__">{"resolvedServerColorMode":"day"}</script></div> </react-partial> <input type="hidden" data-csrf="true" 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