{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:53:49Z","timestamp":1750308829516,"version":"3.41.0"},"publisher-location":"Cham","reference-count":10,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319590622"},{"type":"electronic","value":"9783319590639"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We demonstrate a technique allowing for constant-time calculation of low order Fourier moments, applicable in detection tasks. Real and imaginary parts of the moments can be used as features for machine learning and classification of image windows. The technique is based on a<jats:italic>set<\/jats:italic>of special<jats:italic>integral images<\/jats:italic>, prepared prior to the scanning procedure. The integral images are constructed as cumulative inner products between the input image and suitable trigonometric terms. Additional time invested in the preparation of such integral images is amortized later at the stage of scanning. Then, the extraction of each moment requires only 21 operations, regardless of the number of pixels in the detection window, and thereby is an<jats:italic>O<\/jats:italic>(1) calculation.<\/jats:p><jats:p>As an application example, face detection experiments are carried out with detectors based on Haar-like features serving as opponents to the proposed Fourier-based detectors.<\/jats:p>","DOI":"10.1007\/978-3-319-59063-9_47","type":"book-chapter","created":{"date-parts":[[2017,5,26]],"date-time":"2017-05-26T15:47:16Z","timestamp":1495813636000},"page":"530-543","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Constant-Time Fourier Moments for Face Detection \u2014 Can Accuracy of Haar-Like Features Be Beaten?"],"prefix":"10.1007","author":[{"given":"Przemys\u0142aw","family":"Kl\u0229sk","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,5,27]]},"reference":[{"issue":"1","key":"47_CR1","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/s11263-013-0672-6","volume":"110","author":"J Charles","year":"2014","unstructured":"Charles, J., et al.: Automatic and efficient human pose estimation for sign language videos. 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