Digital Image Correlation: Overview of Principles and Software€¦ · an object produces the same...

Digital Image Correlation: Overview of

Principles and Software

Correlated Solutions, Inc.

2D Image Correlation Fundamentals

Purpose

Basic Idea

Principle

Measuring Displacem.

Introduction

Principle

Photometric Mapping

Displacement Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Limitations, Benefits

Acknowledgments

Conclusions

Outline

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Introduction

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Purpose

Deformation

measurement

▫ Full-field

measurement

▫ Non-intrusive

▫ Planar specimen only

▫ No out of plane motion

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Purpose

▫ Large range of size scales

(10-9 to 102 m.)

▫ Large range of time scales

(static to 200MHz)

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Monocular (cyclopean)

vision cannot determine

the size of objects

▫ Consequence: a 200%

isotropic deformation of

an object produces the

same image as if the

object was moved to one-

half its original distance

from the visual sensor

▫ We must assume the

object is planar, parallel

to and at a constant

distance from the visual

sensor during the entire

experiment

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Image Correlation Technique

▫ How? Given a point and its signature in the

undeformed image, search/track in deformed

image for the point which has a signature which

maximizes a similarity function

Time t Time t”Time t’

trackingtracking

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

▫ In practice, a single value is not a unique

signature of a point, hence neighboring pixels

are used

▫ Such a collection of pixel values is called a

subset or window

Time t Time t’

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

▫ The uniqueness of

each signature is

only guaranteed if

the surface has a

non repetitive,

isotropic, high

contrast pattern

▫ Random textures

fulfill this constraint

(speckle pattern)

Repetitive

Anisotropic

High-contrast

Non-repetitive

Anisotropic

High-contrast

Non-repetitive

Isotropic

Low-contrast

Non-repetitive

Isotropic

High-contrast

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Matching by DIC

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example

▫ The camera acquires 9x9 pixel images

▫ The specimen is marked with a cross-like pattern

Pixels

Image, on screen

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example

▫ White pixels are gray level 100

▫ Black pixels are gray level 0

▫ An image is a matrix of natural integers

100 100 100 100 100 100

Image, on screenImage, in memory

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example

▫ The specimen moves such that its image moves 1 pixel up

and right

100 100 100 0 100 100

0 0 0 0 0 0

100 100 100 0 100 100

100 0 0

0 100 100

100 100 100

Image after motion, on screenImage after motion, in memory

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example: we define a 5x5 subset in the reference image

(before motion)

▫ Problem: find where the subset moved (matching)

100 100 100 100 100 100

Image before motion

100 100 100 0 100 100

0 0 0 0 0 0

100 100 100 0 100 100

100 0 0

0 100 100

100 100 100

Image after motion

Subset

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Solution: check possible matches at several locations and use a similarity score (correlation function) to grade them

▫ Classic correlation function: sum of squared differences (SSD) of the pixel values (smaller values = better similarity)

* )),(),((),,,( jvyiuxIjyixIvuyxCn

Correlation function

Pixel coord., reference image

Displacement (disparity)

n: subset size (9 in our example)

Image before motion Image after motion

Pixel value at (x+i; y+j) Pixel value at (x+u+i; y+v+j)

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example: subset at (x;y)=(5;5), displacement candidate (u;v)=(-2;-2)

* ))25,25()6,5(()2,2,5,5( jiIjiICji

100 100 100 100 100 100

100 100 100 0 100 100

0 0 0 0 0 0

100 100 100 0 100 100

100 0 0

0 100 100

100 100 100

(x;y)=(5;5)

(u;v)=(-2;-2)

000,18)0100()1000()1000()1000()100100(

)00()1000()1000()1000()1000(

)0100()00()00()00()0100(

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example: subset at (x;y)=(5;5), displacement candidate (u;v)=(1;1)

▫ Better correlation score than candidate (u;v)=(-2;-2) [18,000]Indeed it is the smallest score achieveable (perfect match)

100 100 100 100 100 100

100 100 100 0 100 100

0 0 0 0 0 0

100 100 100 0 100 100

100 0 0

0 100 100

100 100 100

(x;y)=(5;5)

(u;v)=(1;1)

0)1,1,5,5( C

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ In reality, images are corrupted by some noise

▫ The SSD function will likely never be 0 for a perfect match

103 101 99 105 100 96

101 104 98 101 98 100

103 96 99 102 103 98

98 101 102 96 97 102

97 98 103 103 98 100

102 99 101 104 102 101

99 100 101 2 100 102

101 97 98 0 96 102

0 1 3 1 2 0

97 99 100 0 97 101

101 103 98 1 99 96

102 99 96 3 102 100

102 3 0

101 1 2

101 3 2

101 0 1

103 2 3

103 0 2

1 102 101

101 100 100

Image before motion Image after motion

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Principle

▫ Example

▫ The specimen moves such that its image moves 0.5

pixel to the right

▫ Need to interpolate the image at non-integer locations

103 101 99 55 100 96

101 104 98 51 98 100

103 96 99 52 103 98

98 101 102 46 97 102

97 98 103 53 98 100

102 99 101 54 102 101

52 0 1

51 4 3

49 2 2

52 1 0

51 2 0

48 0 0

Perfect match

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Photometric Mapping

▫ During image acquisition:

▫ Lighting conditions may change

▫ Sensor integration time adjusted

▫ Pattern may become lighter/darker when

expanded/compressed

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Photometric Mapping

▫ The photometric mapping is not

guaranteed to be an identity, hence the

DIC algorithm may have false matches

▫ Solution: model the photometric

transformation and use it to design a

robust correlation function

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

▫ General circumstances:

▫ The subset in the deformed image has changed

shape, e.g. a square initial subset is likely to be non-

square

Time t Time t’Specimen deformation

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

▫ Solution: model this displacement

transformation (called subset shape function)

and use it to define the deformed subset

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Image Interpolation

▫ Optimization algorithms require the criterion

to be continuous over its parameter space

▫ Images are discrete, hence we need to

reconstruct the continuous information by

means of interpolation

▫ B-splines are a good choice for that purpose

Raw image Bi-linear B-spline interp. Bi-cubic B-spline interp.

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Summary

Acknowledgments

Conclusions

Purpose

Basic Idea

Principle

Introduction

Principle

Photometric Mapping

Advanced Topics

Matching by DIC

Method

Strain Computation

Acknowledgments

Conclusions

Summary

▫ Matching process

▫ Photometric mapping

▫ Shape function

▫ Implications

Time t Time t”Time t’

trackingtracking

Three-Dimensional Digital Image Correlation

Overview

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Outline

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Principle

Strain Computation

Acknowledgments

Conclusions

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Introduction

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Principle

Strain Computation

Acknowledgments

Conclusions

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Purpose

▫ 3-D shape

▫ Strain map

▫ Full-field measurement

▫ Non-intrusive

▫ Any specimen shape

▫ Any motion

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Purpose

▫ Large range of size

scales

(10-9 to 102 m.)

3-D shape of letter „R‟ from “E PLURIBUS UNUM” on U.S. Penny coin using a Scanning Electron

Microscope

1X 50X 200X

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Basic Idea

▫ Much like human

vision, two imaging

sensors provide

enough information to

perceive the

environment in three-

dimensions

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Basic Idea

▫ DIC for stereo-

matching: two

3-D shapes

▫ DIC for

tracking:

relates the two

3-D shapes

through time

Temporal matching

(tracking)

Matching

by stereo-correlation

Matching by

stereo-correlation

3-DTime t

Time t’

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Principle

▫ Monocular (cyclopean)

vision cannot resolve

for the scale of

objects

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Principle

▫ Recovering the three-

dimensional structure

of the environment

using two imaging

sensors is called

stereo-triangulationObject coordinate

system

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Principle

▫ Stereo-

triangulation

requires computing

the intersection of

two optical rays

▫ Feasible only if

these rays are

formulated in a

common coordinate

system

▫ We need to model

and calibrate the

stereo-rig

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Calibration

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Principle

Strain Computation

Acknowledgments

Conclusions

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Perspective projection

Rigid transform Perspective projection

▫ Model: one extrinsic rigid transformation,

two intrinsic perspective projections

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Data Acquisition

▫ Acquire pairs of

images of a special

target undergoing

arbitrary motions

▫ Calibration is shape

measurement process

(bundle-adjustment)

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Parameter Estimation

▫ Dedicated pattern

recognition algorithm

Stereo RigTarget

3-D points

(approx.

known)

Pairs of

2-D points

(auto-recognized)

Transfer function

▫ Identification of the

transfer function Calibration target examples

Left: raw image, right: automatic pattern

recognition

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Parameter Estimation Techniques

▫ Bundle Adjustment

▫ No knowledge of calibration target required

aside from a scale.

▫ Shape of the target is measured during calibration.

▫ Typically, a relatively flat target is used for

initialization through a linear method.

▫ Generally regarded as the optimal method to

calibrate cameras.

▫ Complex to implement due to large equation

systems.

▫ Require block matrix solvers to efficiently invert

large equation systems.

▫ Can provide confidence margins on all

parameters estimated.

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Parameter Estimation Techniques

▫ There are only two constraints required

to accomplish calibration.

1. The calibration target must not deform

between images.

2. A distance between two points on the

target must be known.

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Principle

Strain Computation

Acknowledgments

Conclusions

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

3-D Reconstruction

▫ 3-D Shape Measurement given a pair of images

Temporal matching

(tracking)

Matching

Matching by

stereo-correlation

3-DTime t

Time t’

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

3-D Reconstruction

Two steps:

1. Stereo-correlation

2. Stereo-triangulation

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Tracking: Similar to 2-D DIC

▫ Allow to

relate 3-D

shapes

through

▫ Algorithms

similar to

2-D DIC

Temporal matching

(tracking)

Matching

Matching by

stereo-correlation

3-DTime t

Time t’

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Combining everything

▫ The technology

behind 3-D DIC

▫ Stereo-correlation

▫ Tracking by

correlation

▫ Stereo-

triangulation

(needs

calibration)

Temporal matching

(tracking)

Matching

Matching by

stereo-correlation

3-DTime t

Time t’

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Combining everything

▫ Example

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Principle

Strain Computation

Acknowledgments

Conclusions

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Principle

▫ Strains are computed from the measured

displacements of object points

(strains displacements)

3-D shape at time t

3-D shape at time t’

3-D displacement

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Principal

▫ Strains are only defined in the tangential

plane of the surface.

▫ The DIC data can be converted to a

triangular mesh.

▫ Since triangles are planar by definition, it

is simple to compute the strain on each

triangle.

▫ Same equations as found

in FEM.

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Smoothing

▫ The strains computed on each triangle are

noisy, unless the triangles are fairly large.

▫ The strains are normally smoothed using

low-pass filters.

▫ Low-pass filtering decreases spatial

resolution.

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Conclusions

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Principle

Strain Computation

Summary

Acknowledgments

Conclusions

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Purpose

Basic Idea

Camera Convention

Principle

Introduction

Estimation

Calibration

Stereo Matching

Tracking

Stereo Tracking

Lens Distortion

Matching by DIC

Acknowledgments

Conclusions

Principle

Strain Computation

Summary

▫ Matching process – identical to 2D

▫ Combining matching with triangulation

▫ Combining triangulation with tracking

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