{"id":15150,"date":"2022-06-18T20:18:09","date_gmt":"2022-06-19T00:18:09","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=15150"},"modified":"2026-06-08T13:54:19","modified_gmt":"2026-06-08T17:54:19","slug":"tr-258-moment-preserving-piecewise-linear-approximations-of-signals-and-images","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1994\/tr-258-moment-preserving-piecewise-linear-approximations-of-signals-and-images\/","title":{"rendered":"TR-258: Moment-Preserving Piecewise Linear Approximations of Signals and Images"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-258: Moment-Preserving Piecewise Linear Approximations of Signals and Images\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1994\/\">Technical Report<\/a>\u00a0<strong>TR-258<\/strong><br>December 1994<\/p>\n\n\n\n<h2 id=\"moment-preserving-piecewise-linear-approximations-of-signals-and-images\" class=\"wp-block-heading\">Moment-Preserving Piecewise Linear Approximations of Signals and Images<\/h2>\n\n\n\n<p>Thai B. Nguyen &amp; John Oommen<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>Approximation techniques are an important aspect of digital signal and image pro\u00adcessing. Many lossy signal compression procedures such as the Fourier transform and discrete cosine transform are based on the idea that a signal can be represented by a small number of transformed coefficients which are an approximation of the original.<br>Existing approximation techniques approach this problem in either a time\/spacial domain or transform domain, but not both. This paper reviews various existing approxi\u00admation techniques. Subsequently, we present a new strategy to obtain an approximation ]( x) off ( x) in such a way that it is reasonably close to the original function in the do\u00admain of the variable x, and exactly preserves some properties of the transformed domain. In this particular case, the properties of the transformed values that are preserved are geometric moments of the original function. The proposed technique has been applied to one-dimensional functions, two-dimensional planar curves, and two-dimensional images. This paper also provides a reasonably comprehensive survey of the existing time\/spacial and transform domain approximation strategies. .<\/p>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-258.pdf\">TR-258.pdf<\/a><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report\u00a0TR-258December 1994 Moment-Preserving Piecewise Linear Approximations of Signals and Images Thai B. Nguyen &amp; John Oommen Abstract Approximation techniques are an important aspect of digital signal and image pro\u00adcessing. Many lossy signal compression procedures such as the Fourier transform and discrete cosine transform are based on the idea that a signal can be [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11914,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[],"class_list":["post-15150","page","type-page","status-publish","hentry"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15150","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=15150"}],"version-history":[{"count":3,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15150\/revisions"}],"predecessor-version":[{"id":24394,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/15150\/revisions\/24394"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11914"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=15150"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=15150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}