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Our approach takes its main inspiration from the well\u2010established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi\u2010scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high\u2010frequency details on a shape, the proposed method reconstructs and transfers <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/cgf14180-math-0001.png\" xlink:title=\"urn:x-wiley:01677055:media:cgf14180:cgf14180-math-0001\"\/>\u2010functions more accurately than the Laplace\u2010Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large\u2010scale shape matching. An extensive comparison to the state\u2010of\u2010the\u2010art shows that it is comparable in performance, while both simpler and much faster than competing approaches.<\/jats:p>","DOI":"10.1111\/cgf.14180","type":"journal-article","created":{"date-parts":[[2020,11,3]],"date-time":"2020-11-03T13:09:54Z","timestamp":1604408994000},"page":"165-179","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Wavelet\u2010based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis"],"prefix":"10.1111","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9154-3032","authenticated-orcid":false,"given":"Maxime","family":"Kirgo","sequence":"first","affiliation":[{"name":"LIX \u2010 \u00c9cole Polytechnique \u2010 IP Paris"},{"name":"EDF R&amp;D"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2790-9591","authenticated-orcid":false,"given":"Simone","family":"Melzi","sequence":"additional","affiliation":[{"name":"LIX \u2010 \u00c9cole Polytechnique \u2010 IP Paris"},{"name":"University of Rome La Sapienza"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2276-9553","authenticated-orcid":false,"given":"Giuseppe","family":"Patan\u00e8","sequence":"additional","affiliation":[{"name":"IMATI CNR"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0091-7241","authenticated-orcid":false,"given":"Emanuele","family":"Rodol\u00e0","sequence":"additional","affiliation":[{"name":"University of Rome La Sapienza"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5867-4046","authenticated-orcid":false,"given":"Maks","family":"Ovsjanikov","sequence":"additional","affiliation":[{"name":"LIX \u2010 \u00c9cole Polytechnique \u2010 IP Paris"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2020,11,3]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1137\/140977680"},{"key":"e_1_2_10_3_1","first-page":"1626","article-title":"The wave kernel signature: A quantum mechanical approach to shape analysis","author":"Aubry M.","year":"2011","journal-title":"Conf. on Computer Vision Workshops"},{"key":"e_1_2_10_4_1","volume-title":"Numerical Geometry of Non\u2010Rigid Shapes","author":"Bronstein A. 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