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The method integrates smoothing B-splines into DiffVG via a linear mapping, enabling gradient-based backpropagation of image-space losses to spline key points. Derivative-based smoothing costs support fidelity–simplicity tradeoffs, while stroke width as a third curve dimension allows smooth radius variation and adjustable visible-stroke counts. Experiments demonstrate four stylized vector generation applications, including stroke-based and closed-area abstraction, geometric stylization, and stylized text.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/neural-image-abstraction-using-long-smoothing-b-splines/153107/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/neural-image-abstraction-using-long-smoothing-b-splines/153107.png","ImageObject",300,407,{"name":92,"@type":93},"Sage","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-17","2026-08-27",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How does the method enable optimization of long, smooth curves in differentiable vector graphics?","Question",{"text":112,"@type":113},"It integrates smoothing B-splines into the DiffVG differentiable rasterization pipeline using a linear mapping from B-splines to piecewise cubic Bézier curves, so image-space gradients backpropagate to spline key points.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Why are B-splines useful compared with directly optimizing Bézier curves?",{"text":117,"@type":113},"B-spline parametrizations provide inherent continuity constraints, whereas existing approaches that optimize Bézier segments typically lack guarantees of continuity across segments even with smoothing penalties.",{"name":119,"@type":110,"acceptedAnswer":120},"What are the four applications demonstrated in the document?",{"text":121,"@type":113},"The document demonstrates stylized vector generation using four applications: stylized space-filling path generation, stroke-based image abstraction, closed-area image abstraction, and stylized text generation.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},153107,1787871057,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":41,"preview_page_count":4},687197207057,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","arXiv :2511 .05360v1 [ cs .GR] 7 Nov 2025  \nNeural Image Abstraction Using Long Smoothing B-Splines  \nDANIEL BERIO, Goldsmiths, University of London, United Kingdom MICHAEL STROH, University of Konstanz, Germany  \nSYLVAIN CALINON, Idiap Research Institute, Switzerland  \nFREDERIC FOL LEYMARIE, Goldsmiths, University of London, United Kingdom OLIVER DEUSSEN, University of Konstanz, Germany  \nARIEL SHAMIR, Reichman University, Israel  \nFig. 1. Our method allows to optimize long and smooth B-Spline curves using DiffVG rasterization pipelines. Applications range from text stylization to image abstraction and vectorization.  \nWe integrate smoothing B-splines into a standard differentiable vector graphics (DiffVG) pipeline through linear mapping, and show how this can be used to generate smooth and arbitrarily long paths within image-based deep learning systems. We take advantage of derivative-based smoothing costs for parametric control of fidelity vs. simplicity tradeoffs, while also enabling stylization control in geometric and image spaces. The proposed pipeline is compatible with recent vector graphics generation and vectorization methods. We demonstrate the versatility of our approach with four applications aimed at the generation of stylized vector graphics: stylized space-filling path generation, stroke-based image abstraction, closed-area image abstraction, and stylized text generation.  \nCCS Concepts: • Computing methodologies → Non-photorealistic rendering; Rasterization; Parametric curve and surface models; Neural networks; • Applied computing → Fine arts.  \nAdditional Key Words and Phrases: Differentiable vector graphics, B-splines, Diffusion, CLIP, Long strokes  \nACM Reference Format:  \nDaniel Berio, Michael Stroh, Sylvain Calinon, Frederic Fol Leymarie, Oliver Deussen, and Ariel Shamir. 2025. Neural Image Abstraction Using Long  \nAuthors’ Contact Information: Daniel Berio, Goldsmiths, University of London, London, United Kingdom, [daniel.berio@gold.ac.uk](daniel.berio@gold.ac.uk); Michael Stroh, University of Konstanz, Konstanz, Germany, [michael.stroh@uni-konstanz.de](michael.stroh@uni-konstanz.de); Sylvain Calinon, Idiap Research Institute, Martigny, Switzerland, [sylvain.calinon@idiap.ch](sylvain.calinon@idiap.ch); Frederic Fol Leymarie, Goldsmiths, University of London, London, United Kingdom, [ffl@gold.ac.uk](ffl@gold.ac.uk); Oliver Deussen, University of Konstanz, Konstanz, Germany, oliver.deussen@uni-konstanz.de; Ariel Shamir, Reichman University, Herzliya, Israel, [arik@runi.ac.il](arik@runi.ac.il).  \nThis work is licensed under a Creative Commons Attribution 4 .0 International License.© 2025 Copyright held by the owner/author(s) .  \nACM 1557-7368/2025/12-ART225  \n[https://doi.org/10.1145/3763345](https://doi.org/10.1145/3763345)  \nSmoothing B-Splines. ACM Trans. Graph. 44, 6, Article 225 (December 2025), 12 pages. [https://doi.org/10.1145/3763345](https://doi.org/10.1145/3763345)  \n1 Introduction  \nhe ability to produce long, smooth curves is central to a variety of design and artistic tasks. These include freehand drawing, sketching, calligraphy, typography, logo design as well as image abstractions into compositions of organic, flowing, orblobby shapes. Our aim is to enable the generation of vector graphic outputs that allow these types of designs, while taking advantage of recent advances in gradient-based image generation, stylization, and understanding.  \nDevelopments in differentiable vector graphics (DiffVG) rasterization have enabled gradient-based optimization methods that leverage complex image-space losses to drive image generation, stylization and abstraction methods. Most existing approaches rely on the method of Li et al. [2020], which implements differentiable rasterization for a large subset of elements of the Scalable Vector Graphics (SVG) standard, including piecewise cubic and quadratic Bézier curves. Most of these methods directly optimize Bézier curves, but even with additional smoothing p","cbCainutDo2ZrI2R","https://ap.wps.com/l/cbCainutDo2ZrI2R","pdf",26211386,12,"English","# Introduction\n## Differentiable vector graphics and related approaches\n## Spline parametrizations and integration into DiffVG\n## Uniform B-splines and smoothing criteria\n## B-spline to Bézier conversion and gradient propagation\n## Stroke width modeling and applications","[{\"question\":\"How does the method enable optimization of long, smooth curves in differentiable vector graphics?\",\"answer\":\"It integrates smoothing B-splines into the DiffVG differentiable rasterization pipeline using a linear mapping from B-splines to piecewise cubic Bézier curves, so image-space gradients backpropagate to spline key points.\"},{\"question\":\"Why are B-splines useful compared with directly optimizing Bézier curves?\",\"answer\":\"B-spline parametrizations provide inherent continuity constraints, whereas existing approaches that optimize Bézier segments typically lack guarantees of continuity across segments even with smoothing penalties.\"},{\"question\":\"What are the four applications demonstrated in the document?\",\"answer\":\"The document demonstrates stylized vector generation using four applications: stylized space-filling path generation, stroke-based image abstraction, closed-area image abstraction, and stylized text generation.\"}]","Neural Image Abstraction Using Long Smoothing B-Splines | PDF"]