The document describes a digital image projection (DIP) technique for measuring 3D shapes. The technique projects a reference image onto a target and uses a camera to capture deformed images as the target moves or changes shape. It then uses cross-correlation between images to determine displacement fields and a least-squares solution to calculate displacement-to-height factors, allowing reconstruction of the 3D shape with an average error of 0.04mm. The technique was validated on a spherical cap model.

1. Develop of Digital Image Projection (DIP) technique
h
Projector Camera
M N
D
CA B
s
d
Reference plate
𝒉 = 𝑩𝑫 ≈
𝒔
𝒅
𝑪𝑨 = 𝑲𝑪𝑨
Schematic diagram of digital image projection (DIP) technique
Displacement to height relation:
Camera
Projector
Vertical
Translation
Stage
Target plate
Host computer
Z
Y
X
Displacement vectorReference image
Sketch of displacement to height
Displacement-to-height factor map
Displacement-to-height factor K was obtained using a least-
squares solution of 8–10 images with different height.
The displacement field 𝑪𝑨 can be obtained from cross-
correlation between the deformed image and reference image

2. 20mm
4mm
Spherical cap model
Mean error (mm) STD(mm)
DIP 0.04 0.04
3D shape reconstruction Measurement error
Develop of Digital Image Projection (DIP) technique
Zhang K, Zhang S, Rothmayer A, Hu H, “Development of a Digital Image Projection Technique to
Measure Wind-Driven Water Film Flows”, 51st AIAA Aerospace Sciences Meeting, Grapevine,
Texas, USA, 07 - 10 January 2013.
Validation of digital image projection (DIP) technique: