{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,23]],"date-time":"2023-10-23T13:41:39Z","timestamp":1698068499149},"reference-count":20,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2005,10,20]],"date-time":"2005-10-20T00:00:00Z","timestamp":1129766400000},"content-version":"vor","delay-in-days":5437,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int J Imaging Syst Tech"],"published-print":{"date-parts":[[1990,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The objective of this work is to develop automated techniques for recognizing the same objects in images that differ in scale, tilt, and rotation. Such perspective transformations of images are produced when aerial images of the same scene are taken from different vantage points. The algebraic methods developed previously do not utilize the intensity values of the images, i.e., their pixel gray levels. Since image features essential for object recognition, such as edges and local image textures, may be described in terms of derivatives and integrals of the image intensity, it is necessary to investigate whether certain differential and integral operators applied to different perspective views of the same object are also invariant under the perspective transformation. We proceed to derive new differential operators and their corresponding integral invariants for curves and planar objects. We introduce a variant form of Fourier expansion specially adapted to the projective transformation. Extensions to three dimensions are discussed, as well as applications to other image formation models such as synthetic aperture radar (SAR). These results are steps toward a computational model for perspective\u2010independent object recognition.<\/jats:p>","DOI":"10.1002\/ima.1850020406","type":"journal-article","created":{"date-parts":[[2007,3,5]],"date-time":"2007-03-05T22:45:49Z","timestamp":1173134749000},"page":"296-314","source":"Crossref","is-referenced-by-count":3,"title":["Invariants under image perspective transformations: Theory and examples"],"prefix":"10.1002","volume":"2","author":[{"given":"Eamon B.","family":"Barrett","sequence":"first","affiliation":[]},{"given":"Paul M.","family":"Payton","sequence":"additional","affiliation":[]},{"given":"Michael H.","family":"Brill","sequence":"additional","affiliation":[]},{"given":"Nils N.","family":"Haag","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,10,20]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0734-189X(83)90055-5"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1117\/12.23565"},{"key":"e_1_2_1_4_2","unstructured":"L.NielsenandG.Sparr \u201cProjective area invariants as an extension of the cross\u2010ratio \u201d in Proceedings of the 6th Scandinavian Conference on Image Analysis (SCIA). 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