Laser line extraction with sub-pixel accuracy for 3D measurements

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Laser line extraction with sub-pixel accuracy for

3D measurements

Department of Mathematics, Linköping University Mirjam Mattsson

LiTH-MAT-EX–2020/06–SE

Credits: 30 Level: A

Supervisor: Andrew Ross Winters,

Department of Mathematics, Linköping University Examiner: Fredrik Berntsson,

Department of Mathematics, Linköping University Linköping: August 2020

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Abstract

One 3D measurement method is laser scanning. By projecting and photograph-ing a laser line, the centre line coordinates of the laser can be obtained with centre line detection methods and then be used to generate 3D model of the scanned object. This thesis compares three centre line detection algorithms with respect to their utility for the purpose of 3D reconstruction. The inves-tigated algorithms were Steger’s method, Gaussian fitting and Centre of Mass. The algorithms were evaluated regarding noise sensitivity and their ability to detect jagged laser lines. It was concluded that Steger’s method was the most noise resistant, but less accurate than the others when the jagged line was at an acute angle. The performance of the Gaussian fitting and Centre of Mass algorithms was relatively equal for all investigated test cases.

Keywords:

laser line extraction, Steger’s method, Gaussian fitting, Centre of Mass URL for electronic version:

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Acknowledgements

I would like to extend my sincere thanks to the company I have worked at, for the opportunity to produce my thesis with you. Special thanks to my supervisor and colleagues for many helpful discussions throughout this process. I also wish to express my deepest gratitude to my supervisor Andrew Ross Winters at the Department of Mathematics at Linköping University for guidance and valuable input throughout the work of this thesis.

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List of Figures

1.1 Example of test images with a single vertical laser line . . . 2 1.2 Greyscale for pixel value assignment . . . 3 2.1 Intensity profile of a particular row of a test image . . . 8 2.2 Gaussian function fitted to data points ˜Iil(x) from test image

data which was previously presented . . . 9 2.3 Laser line centre coordinate xic estimated using centre of Mass

given a set of data points ˜Iil(x) . . . 11

2.4 Example of 8-connected neighbourhood with tangential direction ˜

α = 0 . . . 12 3.1 MSE fitting example for a test image . . . 16 3.2 Setup for sharp edge detection . . . 17 4.1 Set 1, images of a laser line at exposure times of increasing length 20 4.2 Zoom in on the lines at the same location in the test images from

Figure 4.1 . . . 20 4.3 Polynomial degree of the fitted function f (y) for two test images

plotted against the MSE . . . 21 4.4 MSE result for test images in Set 1 . . . 22 4.5 MSE result for test images in Set 2 . . . 22 4.6 Test images for sharp edge detection with varying angle edges,

(a) and (b) contain obtuse angles and (c) and (d) contain acute angles. . . 23 4.7 Zoom in on Edge 1, an obtuse angle, for sharp edge comparison . 24 4.8 Zoom in on Edge 2, an obtuse angle, for sharp edge comparison . 24 4.9 Zoom in on Edge 3, an acute angle, for sharp edge comparison . 25 4.10 Zoom in on Edge 4, an acute angle, for sharp edge comparison . 25

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Chapter 1

Introduction

This chapter gives an introduction to the thesis problem. In Section 1.1 the background of the topic is presented, and Section 1.2 gives a more thorough description of the problem for this thesis.

1.1 Background

There are many applications in which 3D measurements are useful, such as industrial design [1]. Such 3D measurement techniques can be divided into two categories: contact and non-contact methods. For contact methods, the measurement instrument is directly placed on the object of interest. These methods are often very precise, but risk to damage the measured object [2] and have a high operational time compared to non-contact methods [3].

Non-contact methods, on the other hand, like CT scanning, photogrammetry, laser radar or laser line projection [4], refer to methods where the measurement instrument is not directly placed on the object of interest. Non-contact methods are often not as accurate as contact methods [3], but are faster and do not risk harm of the measured object. In practice, it is therefore desirable to construct a non-contact 3D measurement method with accuracy comparable to contact methods, that operates faster and avoids damaging of the object.

One way to perform non-contact 3D measurements of an object is by projecting laser light onto it. A camera then captures the reflected and scattered light as a 2D image. When the 2D coordinates for the projected laser line are known along with information about the real world setup, 3D reconstruction techniques, such

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2 Chapter 1. Introduction

as triangulation [5] or epipolar geometry [6], can be used to recover a 3D image of the object. For the 3D coordinates to be accurate, it is important that the 2D coordinates of the laser line are precise.

To extract accurate 2D coordinates of the laser line, it is the centre of the projected laser line that is of interest. There exist methods that, given a 2D image with a projected laser line, extract the centre of the laser line at sub-pixel accuracy. The aim of this thesis is to compare three such centre line extraction algorithms.

1.2 Problem description

The purpose of this thesis project is to implement and compare three laser line extraction algorithms. The algorithms were evaluated on a set of test images of types presented in Figure 1.1. The test images have the properties that they have one projected laser line and the laser is projected in the vertical direction.

(a) Straight (b) Jagged

Figure 1.1: Example of test images with a single vertical laser line

The test images are represented as 2D arrays of 8 bit greyscale values. That is, each pixel in the image is described with a value between 0-255, where each value corresponds to a colour according to Figure 1.2.

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1.2. Problem description 3

Figure 1.2: Greyscale for pixel value assignment

To research the possibility of creating an accurate non-contact 3D measurement method based on laser line projection, three 2D centre line detection algorithms are presented and compared to each other with respect to their utility for the purpose of 3D reconstruction.

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Chapter 2

Theory

This chapter presents the theory behind three methods of laser stripe extraction. Section 2.1 describes three numerical techniques to identify the centre coordi-nates. Section 2.2 then gives a procedure to link extracted laser line points.

2.1 Laser line centre extraction

This section presents three algorithms for extracting the centre points of the pro-jected laser lines. The algorithms are Steger’s method, Section 2.1.1, Gaussian fitting, Section 2.1.2, and Centre of Mass, Section 2.1.3.

2.1.1 Steger’s method

Steger’s method calculates the approximate normal direction of each pixel in an image by estimating the image’s first and second partial derivatives [7]. The normal directions are then used to search for local extreme points along the normal lines to each pixel in the image. Let the image be denoted by I(x, y), where each pixel value (x, y) corresponds to a value between 0 and 255. The derivatives are estimated by convolving the image I(x, y) with two dimensional Gaussian kernels.

The image is estimated as:

r(x, y) = g(x, y) ∗ I(x, y), (2.1)

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6 Chapter 2. Theory

where g(x, y) is a 2D Gaussian kernel,

g(x, y) = 1 2πσ2exp −x 2_{+ y}2 2σ2 . (2.2)

According to Steger, σ in the Gaussian kernel should satisfy:

σ ≥ √w

3, (2.3)

where w is the half width of the laser line.

Convolutions hold the following useful property with regards to differentiation:

(f ∗ h)0 = f0∗ h = f ∗ h0, (2.4)

where prime is either x or y differentiation.

From (2.4), the convolution between the image and its respective Gaussian kernel derivative can, thus, be used to estimate the first derivatives, rx, ry,

and second partial derivatives, rxx, rxy, ryy, of the image. These second partial

derivatives are then used to construct an approximate Hessian matrix for each point in the image:

H(x, y) =rxx(x, y) rxy(x, y) rxy(x, y) ryy(x, y)

. (2.5)

The normal direction for each pixel is then approximated as the normalised eigenvector corresponding to the eigenvalue with maximum absolute value of the Hessian matrix, i.e. n = ˆvmax, where Hvmax = λmaxvmax and λmax =

max(|λ1|, |λ2|).

To identify potential centre line points, the behaviour of the estimated image along the normal line of each pixel is examined. In order for a pixel to hold a local extrema, the first derivative must vanish along the normal line within the pixel. As described in Section 1.2, the laser line in an image holds a high function value. Hence, the point where the derivative vanishes is considered a potential centre line point if the local extrema is a maximum.

Let the normal direction for a pixel (x0, y0) be denoted n = (a, b)T. The normal

line to the pixel can then be expressed as nt = (a, b)Tt = (at, bt)T

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2.1. Laser line centre extraction 7

The behaviour of the estimated image r(x, y) along the normal line of a pixel (x0, y0) can be approximated with the multidimensional Taylor expansion at

pixel (x0, y0) along the normal line (at, bt)T as:

r(x0+ at, y0+ bt) = r(x0, y0) + arx(x0, y0)t + bry(x0, y0)t+ abrxy(x0, y0)t2+ 1 2a 2_r xx(x0, y0)t2+ 1 2b 2_r yy(x0, y0)t2+ O(t3). (2.6)

To determine if the first directional derivative vanishes along the normal line, the derivative of the truncated Taylor polynomial (2.6) with respect to t is investigated, rt(x0+at, y0+bt) = 0 =⇒ t = − arx(x0, y0) + bry(x0, y0) a2_r xx(x0, y0) + 2abrxy(x0, y0) + b2ryy(x0, y0) .

The estimated image has a local maximum at the point (x0+ at, y0+ bt) if

a2rxx(x0, y0) + 2abrxy(x0, y0) + b2ryy(x0, y0) < 0. (2.7)

Since the point (x0, y0) lies in the centre of the pixel, it must be that

(at, bt) ∈ −1 2, 1 2 × −1 2, 1 2 (2.8)

in order for the point (x0+ at, y0+ bt) to lie within the pixel.

In summary, the normal directions ni= (ai, bi)T for all pixels (xi, yi) ∈ I(x, y)

are estimated and the points (xi+ aiti, yi+ biti) that satisfies (2.7) and (2.8) are

considered potential line centre points. How the potential line centre points from Steger’s method are handled and connected together to lines is later described in Section 2.2.1.

2.1.2 Gaussian fitting

The Gaussian fitting method utilises the fact that the intensity profile perpen-dicular to the laser line can be modelled with a Gaussian function [8]. Since the laser lines in the test images are vertically orientated, the intensity of the image

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8 Chapter 2. Theory

is investigated row-by-row. For images with horizontally orientated lines, the image should be investigated column-by-column.

For an image I(x, y) ∈ Rp×q, let row i, i.e. Ii,•, i = 0, 1, .., p − 1 be denoted as

Ii(x).

Figure 2.1(a) shows an example of the intensity profile Ii(x) of a row i in a test

image with a laser line, and Figure 2.1(b) a zoom in on intensity profile of the laser line in that row. The sliced laser line profile is denoted by Iil(x).

(a) Full row (b) Zoom in on laser line in row

Figure 2.1: Intensity profile of a particular row of a test image

The laser intensity profile Iil(x) with n data points is unity-based normalised

with: ˜ Iil(x) = Iil(x) − min Iil(x) max Iil(x) − min Iil(x) . (2.9)

The normalised profile is then used to estimate a Gaussian function:

f (x) = A exp −1 2 x − µ σ 2! , (2.10)

where A = maxxI˜il(x), the mean µ = 1_nP n

k=0xk and the standard deviation

σ = 1_nPn

k=0(xk− µ)2. The estimated Gaussian function (2.10) is then fitted to

the data points in ˜Iil(x) with a least squares fitting technique. Figure 2.2 shows

an example of how a Gaussian function is fitted to the data points from those presented in Figure 2.1(b).

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2.1. Laser line centre extraction 9

Figure 2.2: Gaussian function fitted to data points ˜Iil(x) from test image data

which was previously presented

The mean value of the fitted function in row i, denoted as µif is then used to

estimate the centre line sub-pixel position of the x-coordinate in that row. By iterating through each row i in an image and fitting a Gaussian function to the data points ˜Iil(x), the estimated laser line centre coordinates are given by

(µif, i). How the centre line points from the Gaussian fitting method are linked

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10 Chapter 2. Theory

2.1.3 Centre of Mass

Similar to the Gaussian fitting method, the centre of Mass method estimates the centre line points by examining a normalised laser line profile ˜Iil(x) from

(2.9) of each row i. The centre of mass of a laser line profile is calculated with:

xic= e P j=s j ˜Iil(j) e P j=s ˜ Iil(j) , (2.11)

where s is the first and e the last x-value of ˜Iil(x). By introducing a weighing

function W (x) a weighted centre of mass can be calculated as:

xic= e P j=s jW (j) ˜Iil(j) e P j=s W (j) ˜Iil(j) . (2.12)

If W (x) = ˜Iil(x), the intensity weight increases exponentially [9], which is

de-sirable since the centre line coordinate is more likely to lie in a bright pixel. By estimating the laser line centre x-coordinate xicwith:

xic= e P j=s j ˜Iil(j) 2 e P j=s ˜ Iil(j) 2 , (2.13)

for each row i, the estimated laser line centre coordinates are given by (xic, i).

How the centre line points are linked to lines is later described in Section 2.2.2. Figure 2.3 shows an example of an estimated xic given a laser line intensity

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2.2. Line linking 11

Figure 2.3: Laser line centre coordinate xicestimated using centre of Mass given

a set of data points ˜Iil(x)

2.2 Line linking

This section describes how the line centre points are linked to lines for the different centre line detection algorithms. Section 2.2.1 describes the Steger’s line linking method, which links the potential centre line points detected with Steger’s method to lines and Section 2.2.2 presents a line linking method for the Gaussian fitting and centre of Mass algorithms.

2.2.1 Steger’s linking algorithm

With Steger’s method described in Section 2.1.1, potential line centre points (xi + aiti, yi + biti) are extracted. For each potential line centre point the

following data is known: the normal ni = (ai, bi) and the second derivative in

direction n , i.e. λmax since nTHn = nTλmaxn = λmaxnTn = λmax. From

the normal ni= (ai, bi) = (cos αi, sin αi), the angle of the tangential direction,

˜ α, is calculated with: ˜ αi= αi+ π 2. (2.14)

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12 Chapter 2. Theory

Lines are linked by starting with the potential line centre point with maximum second derivative, identified from λmax, and adding the best neighbour to the

point. The neighbours are searched for in the tangential directions n⊥_i and −n⊥_i [7].

From a 8-connected neighbourhood, three pixels in the orientation interval [ ˜α − π/8, ˜α + π/8] are examined. For example, if the current point is (cx, cy) and

α = −π₂, then ˜α = 0 gives the orientation interval [−π/8, π/8] and the pixels (cx+ 1, cy− 1), (cx+ 1, cy), (cx+ 1, cy+ 1) are examined, as shown in Figure 2.4

Figure 2.4: Example of 8-connected neighbourhood with tangential direction ˜α = 0

Let the current potential line centre point be denoted with pcand it’s neighbours

with pjn, j = 1, 2, 3. The best neighbour is chosen based on two parameters:

the distance between the current point and the neighbour, dj = kpc− pjnk₂,

and the angle difference between the points βj = |αc− αjn|, βj∈ [0, π/2].

The neighbour j that minimises the value dj + βj is added to the line, and

neighbour pjn is set to be the current point. The algorithm continues until

no best neighbour is found in the neighbourhood. When the line has reached an endpoint in both tangential directions n⊥ and −n⊥, a new start point is selected as before. The algorithm creates new lines as long as there are points that are not linked to a line and have λmax above a certain threshold.

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2.2. Line linking 13

2.2.2 Line linking for Gaussian fitting and Centre of Mass

The Gaussian fitting and Centre of Mass algorithms described in Section 2.1.2 and 2.1.3 store the centre line points in a list ordered by the y-coordinate of the centre line point. The centre line points are linked by starting with the first point in the list. That is, the centre line coordinate with lowest y-coordinate. Let it be denoted by (x0, y0) and let the neighbours of the coordinate be defined as

the line centre coordinates with y-value y0+ 1. The Euclidean distance between

the current coordinate and its neighbours is then calculated.

If the neighbour with the minimum Euclidean distance to the current point is less than a certain threshold, then the neighbour is added to the line and removed from the list of centre line points. Otherwise a new line is created starting with the point with lowest y-coordinate. The latest point that has been added to a line is then set to be the current point and linked by examining its neighbours as before. The linking continues until all points have been connected to lines. Data: centrepoints contain all centre line coordinates ordered by

increasing y-coordinate Result: List with all lines lines = empty list;

line = empty list;

(currX, currY) = centrepoints[0]; while centrepoints do

add (currX, currY) to line;

remove (currX, currY) from centrepoints;

neighbours = centrepoints with y-coordinate currY+1; forall neighbours do

d = Euclidean distance between neighbour and (currX,currY) end

(neighX, neighY) = neighbour with minimum d; if minimum d < threshold then

(currX, currY) = (neighX, neighY); else

add line to lines; line = empty list;

(currX, currY) = centrepoints[0]; end

end

return lines;

Algorithm 1: Pseudocode of the line linking algorithm for Gaussian fitting and Centre of Mass

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Chapter 3

Method

The different algorithms of centre line detection are compared with respect to two aspects: how sensitive the algorithms are to noise and how well they can detect any jagged parts of the laser lines. How well the algorithms can detect the jagged part of the lines will further be referred to as sharp edge detection. This chapter describes the used methods for comparing noise sensitivity, Section 3.1, and how well the algorithms handles sharp edges, Section 3.2.

3.1 Noise sensitivity

To compare the noise sensitivity for the algorithms, a mean square error (MSE) measurement was conducted. A polynomial of degree m,

f (y) =

m

X

k=0

akyk, (3.1)

was fitted to the detected line centre points (xi, yi) of each algorithm with the

least squares method to estimate the x-coordinate given the y-coordinate. The MSE measurement is defined as:

MSE = 1 n n X i=1 |xi− f (yi)| 2 , (3.2) Mattsson, 2020. 15

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16 Chapter 3. Method

where n is the number of line points. Figure 3.1 shows an example of how a polynomial function is fitted to the centre line points detected with the Centre of Mass algorithm.

(a) Line centre points detected with Centre of Mass

(b) Line centre points and a fitted polynomial function

Figure 3.1: MSE fitting example for a test image

The reason why the polynomial estimates the x-coordinate given the y-coordinate is that the lines in the test images are in the vertical direction, hence the x-span is smaller than the y-x-span and it produces a better fit to estimate the x-coordinate given the y-coordinate than vice versa. For horizontally oriented lines it would be more appropriate to estimate the y-coordinate given the x-coordinate.

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3.2. Sharp edge detection 17

3.2 Sharp edge detection

To compare how well the algorithms can detect sharp edges, test images with folded papers of the type Figure 3.2 were considered. The edge where the paper is folded and the laser line changes direction is referred to as a sharp edge.

Figure 3.2: Setup for sharp edge detection

To compare how the algorithms detect these kind of edges, test images were run through the three detection algorithms. The edges were then zoomed into and visually compared.

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Chapter 4

Results

This chapter presents the results for how the three algorithms performed re-garding noise sensitivity, Section 4.1, and sharp edge detection, Section 4.2.

4.1 Noise sensitivity

The mean square error was calculated on two sets, Set 1 and Set 2, containing images of straight laser lines with exposure times of varying length. Set 1 is shown in Figure 4.1 and Set 2, with similar characteristics as Set 1, is not included for the sake of brevity. The images in Set 2 will be referred to as Exposure 1, Exposure 2 and Exposure 3.

The images in both sets are ordered by increasing exposure time. Increased exposure time leads to a laser line of increased intensity. Image 1, 4.1(a), and Exposure 1 has the shortest exposure time and Image 4, 4.1(d), and Exposure 3 has the longest exposure time. The exposure times in Set 1 and Set 2 are, however, not the same. A zoom in on the lines at the same location in the Set 1 test images are shown in Figure 4.2.

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20 Chapter 4. Results

(a) Image 1 (b) Image 2

(c) Image 3 (d) Image 4

Figure 4.1: Set 1, images of a laser line at exposure times of increasing length

(a) Image 1 (b) Image 2 (c) Image 3 (d) Image 4

Figure 4.2: Zoom in on the lines at the same location in the test images from Figure 4.1

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4.1. Noise sensitivity 21

To decide a sufficient degree of the polynomial function, (3.1), to fit to the centre line points the MSEs were calculated by using polynomial fittings of increasing degree from 1-10. A plot of the results on Image 1 and Image 4 for degree 2-10 is presented in Figure 4.3. The MSE for one degree polynomials was too deviant to be meaningful in the plots.

(a) MSE for Image 1 (b) MSE for Image 4

Figure 4.3: Polynomial degree of the fitted function f (y) for two test images plotted against the MSE

A higher degree for the polynomial fitting means that the fitted function has more freedom to adapt to deviant centre line points. This is undesirable since the presence of deviant centre line points are what we want to measure with the MSE. Figure 4.3 shows that the MSE decreases sharply until degree 4 and thereafter marginally decreases for all algorithms. From the results presented in Figure 4.3 and considering that the laser lines in the test images lack curvature we conclude that a polynomial fitting of degree four is appropriate to use for the MSE measurement comparison.

The result of the MSE measurements described in Section 3.1 with a fourth degree polynomial fitting are presented in Figure 4.4 for Set 1 and 4.5 for Set 2.

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Figure 4.4: MSE result for test images in Set 1

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4.2 Sharp edge detection

The sharp edge detection comparison was made on four edges presented in Figure 4.6. Edge 1 and 2, 4.6(a) respectively 4.6(b) are obtuse angles whereas Edge 3 and 4, 4.6(c) respectively 4.6(d) are acute angles.

(a) Edge 1 (b) Edge 2 (c) Edge 3 (d) Edge 4

Figure 4.6: Test images for sharp edge detection with varying angle edges, (a) and (b) contain obtuse angles and (c) and (d) contain acute angles.

Results that presents how well the algorithms detect sharp edge at different angles are shown in Figures 4.7-4.10.

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(a) Centre of Mass (b) Gaussian (c) Steger

Figure 4.7: Zoom in on Edge 1, an obtuse angle, for sharp edge comparison

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Figure 4.9: Zoom in on Edge 3, an acute angle, for sharp edge comparison

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Chapter 5

Discussion and Summary

Figure 4.4 and Figure 4.5 show similar results regarding the order of magnitude of the MSE for the different algorithms, where the Gaussian fitting and Centre of Mass have MSEs around 0.02 − 0.03 and Steger’s algorithm around 0.005 − 0.01. How the exposure time effects the MSE is inconsistent; for Set 1 the MSE increases as the exposure time increases, and for Set 2 the MSE decreases as the exposure time increases. Hence, it is hard to draw any conclusions about how the intensity of the laser line affects the MSE.

However, it is clear that the Steger algorithm has the lowest MSE for all test images, indicating that the Steger algorithm is most noise resistant. This result is reasonable considering that Steger algorithm, as opposed to the Gaussian fitting and Centre of Mass algorithm, applies a Gaussian smoothing kernel onto the original image to approximate the centre line coordinates. In other words, the Steger algorithm extracts the centre line coordinates of a smoothed, noise reduced image, contrary to the other algorithms that approximate the centre line coordinates of the original image.

The fact that the Steger algorithm yields a more noise resistant result also comes from its use of neighbour information. Steger’s algorithm studies the image as a 2D function, where it takes the neighbouring area in both x- and y-direction of a pixel in consideration when approximating the local maximums. In contrast, the Gaussian fitting and Centre of Mass algorithms investigate each row as independent 1D functions - taking only neighbouring pixel information along the x-direction into account.

Algorithms that are sensitive to noise can cause errors in the reconstructed

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28 Chapter 5. Discussion and Summary

ject which makes the accuracy of the 3D measurement questionable. In practice, however, real world images always contain noise. To preprocess the images with noise reduction could improve the Gaussian fitting and Centre of Mass algo-rithm, but such preprocessing could also risk losing valuable information about the image.

For edges with obtuse angles, as in Figure 4.6(a) and 4.6(b), the algorithms detect the edges with similar visual accuracy but the Steger algorithm does extract a smoother line. For edges with acute angles, as in Figure 4.6(c) and 4.6(d), the Centre of Mass and Gaussian fitting algorithms detect a sharper edge than the Steger algorithm. Presumably because of the smoothing kernel applied in the Steger algorithm. The inability to detect the sharpness of the edge will lead to lack of accuracy when the scanned object is reconstructed, and the presence of small details or damages such as scratches might not be detected.

In summary, this thesis presents three centre line detection methods and com-pares them with respect to two aspects: how sensitive they are to noise and how well they can detect sharp edges in the projected laser lines. It is concluded that the Steger algorithm is more noise resistant but less accurate when the laser line creates an edge with acute angles. The results of the Gaussian fitting and Centre of Mass algorithm are relatively equal. To investigate the algorithms further, their performance on 3D reconstructions of objects should be evaluated.

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Upphovsrätt

Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare – från publiceringsdatum under förutsättning att inga extraordinära omständig-heter uppstår.

Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner, skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning och för undervisning. Överföring av upphovsrätten vid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av dokumentet kräver upphovsmannens medgivande. För att garantera äktheten, säkerheten och tillgängligheten finns lösningar av teknisk och administrativ art. Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman i den omfattning som god sed kräver vid användning av dokumentet på ovan beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan form eller i sådant sammanhang som är kränkande för upphovsmannens litterära eller konstnärliga anseende eller egenart.

För ytterligare information om Linköping University Electronic Press se förla-gets hemsida http://www.ep.liu.se/.

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