<p>Surface profilometry is essential in manufacturing, quality control, and biomedical imaging, where precise, noncontact surface measurements are required. Traditional techniques such as digital fringe projection (DFP) face limitations in computational efficiency, noise robustness, and handling complex geometries. This paper explores the integration of DFP and optical flow estimation as a novel approach to 3D surface reconstruction, with the aim of advancing noncontact measurement technologies. The proposed method employs phase-shifted DFP to encode surface depth and combined with optical flow techniques that estimate the pixel displacements between captured frames. A custom simulator developed in Blender 3D enables automated DFP and surface validation under controlled, reproducible conditions. Quantitative results show a normalized mean squared error (NMSE) of 0.056 and a mean error of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16520_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">$6.41\,\text {px}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>6.41</mn> <mspace width="0.166667em" /> <mtext>px</mtext> </mrow> </math></EquationSource> </InlineEquation> for the Sphere model, 0.126/<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16520_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">$2.57\,\text {px}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.57</mn> <mspace width="0.166667em" /> <mtext>px</mtext> </mrow> </math></EquationSource> </InlineEquation> for the Dolphin, and 0.139/<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="170_2025_16520_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">$11.73\,\text {px}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>11.73</mn> <mspace width="0.166667em" /> <mtext>px</mtext> </mrow> </math></EquationSource> </InlineEquation> for the Face. These results demonstrate competitive accuracy on smooth surfaces and highlight challenges with complex geometries. Reconstruction accuracy declines with surface complexity, primarily due to the fact that current dense optical flow models are not optimized for structured light. High-frequency details, object boundaries, and surface discontinuities often lead to local flow estimation errors, reducing accuracy on intricate shapes. Although the method has not yet exceeded traditional techniques in all metrics, it presents a promising alternative for efficient and robust surface reconstruction. This paper outlines the strengths and limitations of the method and proposes improvements to guide the future development and industrial deployment of this scalable framework.</p>

Integration of fringe projection and optical flow for 3D surface reconstruction: a novel simulation-based approach

期刊论文
出版模式：

开放获取
发表日期：

2025年10月1日

查看全文

Aline de Faria Lemos,
Balázs Vince Nagy

摘要

Surface profilometry is essential in manufacturing, quality control, and biomedical imaging, where precise, noncontact surface measurements are required. Traditional techniques such as digital fringe projection (DFP) face limitations in computational efficiency, noise robustness, and handling complex geometries. This paper explores the integration of DFP and optical flow estimation as a novel approach to 3D surface reconstruction, with the aim of advancing noncontact measurement technologies. The proposed method employs phase-shifted DFP to encode surface depth and combined with optical flow techniques that estimate the pixel displacements between captured frames. A custom simulator developed in Blender 3D enables automated DFP and surface validation under controlled, reproducible conditions. Quantitative results show a normalized mean squared error (NMSE) of 0.056 and a mean error of $6.41\,\text {px}$ $6.41 px$ for the Sphere model, 0.126/ $2.57\,\text {px}$ $2.57 px$ for the Dolphin, and 0.139/ $11.73\,\text {px}$ $11.73 px$ for the Face. These results demonstrate competitive accuracy on smooth surfaces and highlight challenges with complex geometries. Reconstruction accuracy declines with surface complexity, primarily due to the fact that current dense optical flow models are not optimized for structured light. High-frequency details, object boundaries, and surface discontinuities often lead to local flow estimation errors, reducing accuracy on intricate shapes. Although the method has not yet exceeded traditional techniques in all metrics, it presents a promising alternative for efficient and robust surface reconstruction. This paper outlines the strengths and limitations of the method and proposes improvements to guide the future development and industrial deployment of this scalable framework.