Landmark detection in DVT scansof the head

Interdisciplinary Project Thesis

Tobias Duewell

June, 2018

Advisors: Prof. Konrad Schindler, Dr. Claudio Rostetter

Institute of Geodesy and Photogrammetry, ETH Zurich

Abstract

This thesis evaluated the detection of landmarks within cone beam com-puter tomography-images. 15 landmarks within a data set of 46 imageswere tested. Two different classifiers (Subspace-KNN- and Bagged-Trees-Ensemble classifier) and three different descriptors were com-pared. For further robustness, a shape model according to Cootes andTaylor [1992] was applied. The detection rate varies, depending on thetested landmark, whereby the easiest landmark to detect (Mandibularnerve (V3)) is found 87% of the time and the least detectable landmark(Arcus zygomaticus) is found 23.5% of the time. Depending on thelandmark, the shape model can increase the detection rate, althoughjust slightly.

i

Contents

Contents iii

1 Introduction 11.1 Conventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Method 32.1 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1.1 Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Shape Model Creation . . . . . . . . . . . . . . . . . . . . . . . 52.3 Sample Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . 62.4 Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.5 Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6 Landmark Detection . . . . . . . . . . . . . . . . . . . . . . . . 10

3 Results and Discussion 133.1 Shape Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.2 Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.3 Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Conclusion 25

Bibliography 27

iii

Chapter 1

Introduction

The localization of landmarks within medical images can be a monotoneand repetitive task. Therefore an automation is a welcome discharge for pro-fessionals.Today, machine learning is used in all kind of data processing, especially incomputer vision. For this study, 50 evaluated images were used to train adetection algorithm for landmarks within the jaw area of the human scull.For additional robustness and improvement of the results, the detection isimproved by the use of an active shape model according to Cootes and Tay-lor [1992].This report describes a pipeline of seven steps that allows a working land-mark detection within cone beam computer tomography images (DVT) (Scarfeand Farman [2008]) of the head.

1. Unification and statisticsThis step ensures an unified data format and records a first statistic ofthe properties of all images.

2. PreprocessingThe extension of each scull is determined, which allows an alignmentof all images. The optional Soble-filter is applied at the images.

3. Shape model creationThe known landmarks of each training image are combined to a shapevector, aligned and computed into a model by principal componentanalysis.

4. Sample extractionPositive and negative data samples are extracted from the training dataset.

5. TrainingAn ensemble classifier is trained with the previously extracted positive

1

1. Introduction

and negative samples.

6. TestingEvaluation of test images, voxel by voxel around a roughly estimatedlandmark position.

7. DetectionThe result of the testing is combined with the shape model to increasethe robustness of the result.

1.1 Conventions

In the following, positions and three dimensional vectors are represented bya small written vector (i.e. ~x). Shape vectors (i.e. ~X) have a dimensionalityof 3 × N, whereby N is the number of landmarks within a shape model,and are represented with a capital letter. Matrices are represented as thickprinted capital letters M.

2

Chapter 2

Method

For this study, 50 cone beam computer tomography (DVT) images of thehuman scull were used. Within each image a medical professional flaggedthe 15 landmarks given in table 2.

ID Name ID Name1 & 2 Mandibular nerve (V3) (left/right) 8 & 9 Processus styloideus (left/right)3 & 4 Inferior alveoary nerve (left/right) 10 & 11 Lateroorbital fissur (left/right)

5 Spina nasalis anterior 12 & 13 Arcus zygomaticus (left/right)6 & 7 Maxillary nerve (V2) (left/right) 14 & 15 Ophthalmic nerve (V1) (left/right)

Table 2.1: List of used landmarks

The coordinate system for each image is set, so x defines the position alongthe axis from nose to occiput, y from the left side to the right side of thescull (patients perspective) and z from the throat to the top of the scull.

All processing was done within Matlab. In addition the SIFT3D C libraryby Rister et al. [2017] was used for creation of sift descriptors.

2.1 Preprocessing

In a first step, the images are transformed from the .dicom1 format intouniform Matlab files. Thereby, a statistic of the maximum and minimumvalues within every image is made. Some images include sculls with im-plants, which have voxels with much higher intensity values then the restof the scull. Influences of those are reduced in a second step: The smallestmaximum value of any image is used as threshold for all images. The in-tensity values are then scaled into a range between

[0, 1]

and reduced intoarrays with single precision2.

1www.dicomstandard.org2https://ch.mathworks.com/help/matlab/ref/single.html

3

2. Method

Figure 2.1: Coordinate system within scull

Figure 2.2: Profile and extensions within an image

The single sculls are not positioned in a consistent way within the images.Therefore, the extension of each scull has to be determined by projecting themaximal intensity values along the x- and then z-axis, respectively, alongthe y- and z-axis. In the resulting intensity profiles, a border is set wherea given threshold is overstepped for the first time. This is not done alongthe z-direction. Due to the existence of brackets within most images, theborder at the occiput is set at the second occurrence of the threshold, ifpresent. Henceforward ~xRel is calculated for the relative position of a land-mark within a scull.

~xRel =

xRelyRelzRel

, with xRel , yRel , zRel ∈[0, 1]

(2.1)

Four of the provided images fit not to the others. After manual inspection, itseems most likely, the ground truth data is faulty. The images are not usedfor further calculations.

4

2.2. Shape Model Creation

2.1.1 Filter

Within an optional step, a Sobel-filter can be applied to the image. In previ-ous tests, it reduced the influence of differences between images with differ-ent intensity patterns.

2.2 Shape Model Creation

The third step within the the processing pipeline is the creation of an activeshape model accorindg to Cootes et al. [1994]. Its purpose is the reductionof false positives by using the positions of other landmarks within the scull.A shape within image i is defined as the composite of the coordinates of allN = 15 landmarks k within the scull.

~Xi =(

xi,1 yi,1 zi,1 xi,2 . . . xi,k yi,k zi,k . . . zi,N)T (2.2)

The creation of the shape model is split into two steps: an iterative alignmentof the training shapes and a principal component analysis.For the alignment an arbitrary training shape is centered around the position~0 normalized and then used as a first reference ~Y1.

~Y1 =~X1 − X1

|~X1 − X1|(2.3)

All remaining training shapes are then aligned with the reference set byapplying the Procrustes algorithm3 (Radke [2015]) resulting in the shapevectors ~Y′i . The mean of the aligned shapes is then used as a new reference.

~Y2 =1N ·∑

Ni=1

~Y′i| 1

N ·∑Ni=1

~Y′i |(2.4)

This step is repeated until |~YI − ~YI−1| <= 10−4. If a given shape has incom-plete data, it has to be reconsidered within the averaging. This results in thedata set

D ={~Y′1, ~Y′2, . . . , ~Y′P

}(2.5)

with number of training shapes P.D is the input for the principal component analysis, which is already pro-vided by Matlab

4.

The given output consists of the principal component coefficients (or modes)represented in the matrix P, the principal component variance λq for each

3https://mathworks.com/help/stats/procrustes.html4https://mathworks.com/help/stats/pca.html

5

2. Method

Figure 2.3: Coverage depending on set Q.

component, the estimated mean shape ~µ and the coverage. The size of P is3P×Q. Any shape within the training set can be represented by the formula

~Xi = R · (PT ·~b +~µ) · s +~c (2.6)

R, s and ~c are rotation matrix, scalar factor and translation vector and canbe determined by the Procrustes algorithm. By decreasing Q, it is possibleto decrease the dimensionality of our problem. The coverage describes thepercentage of the total variance explained by Q principal components and~µ.

For further evaluation of the created shape model, a small visualization tool(Figure 2.4) was written. It enables the inspection of each created shapemodel by transforming the ground truth to the mean shape, which wastrained for the given patient. The user is now able to change manually thenumber of modes Q and the shape coordinates ~b with sliders. In additionshe can define, if a given ground truth is known or not. This allows eval-uation of the inner relations of the shape model. The difference betweenground truth and set model is scaled with the scaling factor s from the trans-formation to the mean shape, which results in the distance within the imagespace.

2.3 Sample Extraction

For the detection of landmarks, a binary classifier is trained. Positive as wellas negative samples are taken from the training data. The positive samplesare extracted form the direct neighbourhood of the ground truth positions

6

2.3. Sample Extraction

Figure 2.4: Shape Model Visualizer

~xi,k +~j.

~j =

uvw

, with u, v, w ∈ {−1, 0, 1} (2.7)

If the landmark has a counterpart on the other side of the head, it is mirroredand used as well. The samples of the Spina nasalis anterior are mirroreddirectly and so used twice. This results in a total number of positve samplesof 2× 27 = 54 per training image.

The negative samples are drawn randomly from the rest of the image, wherebythe probability of extraction decreases with the distance to the ground truth.The position of a negative sample ~xneg is given by

~xneg =

sin α · cos βsin α · sin β

cos α

· |r| · c1 + c2 (2.8)

c1, c2 = const.r ∼ N (0, 1)

α ∼ U (0, 2π)

β ∼ U (0, π)

The coordinates of ~xneg are rounded to the next integer, duplicates and po-sitions outside of the image are replaced by additionally created suitable

7

2. Method

Figure 2.5: Landmark cross sections, from top to bottom: Mandibular nerve (V3) (l/r), (l/r),Spina nasalis anterior, Maxillary nerve (V2) (l/r), Processus styloideus (l/r), Lateroorbital fissur(l/r), Arcus zygomaticus (l/r), Ophthalmic nerve (V1) (l/r)

coordinates. For this study the values c1 = 10 and c2 = 5 are used. Trainingsets with 50, 100, 200, 400 and 800 negative samples per image are tested.The high number of negative samples around the ground truth, should al-low a good distinction from the direct neighbourhood.

Descriptors

Three different descriptors are used. Firstly and secondly the intensityvalues within each extracted sample from the original image or the sobel-filtered image. Thereby the size of the descriptor can be chosen freely. De-scriptor sizes of (5× 5× 5), (9× 9× 9) and (13× 13× 13) are tested. In thefinal evaluation, the descriptor size (9× 9× 9) was used. The third kind ofdescriptor is the SIFT3D-descriptor by Rister et al. [2017]. Its size is deter-mined by its implementation (768 values).Further dimensionality reduction can be achieved by a preceding principalcomponent analysis. Table 2.6 shows the the applied dimensionality reduc-tions and the resulting descriptor sizes.

2.4 Training

The training algorithms are created, tested and compared with the Mat-lab Classification Learner. Table 2.6 shows the accuracy, and confusionmatrix for different type of classification algorithms.

8

2.4. Training

Figure 2.6: Specification of different classifiers. Evaluated with Matlab ClassificationLearner, Mandibular nerve (V3).

For the final evaluation, the Matlab Subspace K-Nearest Neighbour5 (100negative samples per image) and Bagged Trees6 classifier (800 negative sam-ples per image) are used. Since they are ensemble classifiers and we dis-tinguish only between two classes (true and false), we can use continuousresult (between [0, 1]) for further evaluation instead of a binary one. Thetraining parameters were adjusted automatically by using a 5 times crossvalidation.A training set consists of P− 10 = 36 single image sets, which were used totest the remaining 10 images.Table 2.6 shows the details for Mandibular nerve (V3). Other landmarks areless accurate. For example, Arcus zygomaticus has around 1688 false posi-tives instead of 242 when using Bagged Trees and the gray value descriptor.The same can be seen with the SIFT descriptor, but the total number of falsepositives is just 156 instead of 1.

5https://mathworks.com/help/stats/random-subspace-for-increased-classification-accuracy.

html6https://mathworks.com/help/stats/regression-tree-ensembles.html

9

2. Method

2.5 Testing

The surrounding of the rough estimate ~xEsti of a landmark within a testimage was classified voxel by voxel. ~xEsti is calculated from the average ofall relative positions ~xRel i within the training set and the extension of the teststet

~xEsti =

∆bx 0 00 ∆by 00 0 ∆bz

i

·P

∑p=1

~xRel ,p (2.9)

∆bx, ∆by, ∆bz are the scull extension in voxel, as calculated in the preprocess-ing (See 2.1).

The size of the neighbourhood is determined by the variance of the distribu-tion of the relative landmarks positions of the training data.

tested pixels = ~xEsti +

xmymzm

with xm ∈

[−3 · σx, −3 · σx + 1, . . . , −1, 0, 1, . . . , 3 · σx

], etc. When

σ > 50[voxel] the size of the test area is limited to a border of 2× 50 + 1voxel.

2.6 Landmark Detection

From the previous step, an evaluated area for each landmark within an im-age is given. This three dimensional probability matrix Irawwith values inbetween

[0, 1

]is filtered with a median filter7, which results in Imedand

with a Gaussian filter8 (σ = 5) which results in Igauss. The Gauss filter ispreceded by setting all intensity values below 0.3 of the highest probabilitywithin Irawto 0. This is to prevent big areas of medium probability to in-terfere with the shape model. The high standard deviation set within theGaussian filter allows the calculation of a gradient within the test area.The created shape model can help distinguish between false and true pos-itives. To achieve a successful performance, proper initialization positionshave to be established. Depending on the accuracy of the classifier, thisis done in one of three ways. Either the voxel with the highest probabil-ity value of Imedis used, the highest probability value next (R = 35 withBaggedTrees, R = 5 with Subspace KNN) to the rough estimate is used oran iterative process is applied to find the local maximum around the roughestimate. The process works as follows:

7https://mathworks.com/help/images/ref/medfilt3.html8https://mathworks.com/help/images/ref/imgaussfilt3.html

10

2.6. Landmark Detection

For each test area:

1. start at estimated position ~xRel

2. find local maximum within maximal distance R

3. set newly found maximum as new start value

4. repeat from 2, unless no new maximum is found

Further, it is assumed that at least 6 local maxima correspond to the truelandmarks. By try and error, the set with the smallest deviation from themean shape is established and assumed to be true. Method two gives thebest results.

Applying shape model

With those initially estimated shape vector XIt0, the shape model is applied.For every current estimated landmark position, an improvement vector d~xiis calculated. d~xi is given by the difference of the highest value within theneighbourhood (radius R = 3) of the estimate and the estimate positionitself. Their length is adjusted according to Cootes et al. [1994]:

|d~x|′ =

0, |d~x| ≤ δ12 |d~x|, δ < |d~x| < dmax12 dmax, |d~x| ≥ dmax

(2.10)

δ = 0.5dmax = 5

Combined, they result in a shape improvement vector d~X. By applying onceagain the Procrustes algorithm, we fit to the new shape XIt0 + d~X to themean shape. The difference between the fitted new shape and the meanshape X is then used to calculate new shape coordinates:

~b = PT ·(

XIt0 + d~X− X)

(2.11)

or~b =

(PTWP

)−1PTW

(XIt0 + d~X− X

)(2.12)

with the diagonal weight matrix W and the modes P with Q = 10. Theelements of W correspond to the probability value at XIt0 + d~X within thetest area.

To keep the shape in an sensible condition, a constraint according to Cootesand Taylor [1992] is applied. If the Mahalanobis distance Dm is bigger then

11

2. Method

a certain value Dmax = 3.5

D2m =

t

∑i=1

(b2

iλi

)≤ D2

max (2.13)

the shape coordinates are corrected according to Cootes et al. [1994]:

~b→~b ·√

Dmax

Dm(2.14)

By transforming the new shape vector back into the image space, by usingthe previous calculated Procrustes transformation parameters, we receivenew estimate parameters. From there on, we iterate until we reach a stableresult. This position can be improved by looking for the local maximum(R = 5).

12

Chapter 3

Results and Discussion

3.1 Shape Model

Figure 2.3 already shows the coverage within one of the created shape mod-els. The accuracy of the approximation can be seen in figure 3.1. Figure3.2 shows the increase in distance of an approximated positions from theground truth, if all other landmarks are known. This is achieved by exclud-ing the landmark from the Procrustes algorithm, and setting its weight tozero within equation (2.12).

If Q = 9 we have a coverage of more than 90%. This still corresponds toa deviation of around 8 voxel, which is less then 5 voxel in x-,y- and z-direction. The corresponding landmarks on the right and left side of thescull have similar increase in approximation quality, with the only exceptionof landmark 6 (Maxillary nerve (V2)), where the approximation of left andright landmark differs quite a bit.

The Mahalanobis distance Dm is the key value for the constraint during thelocalization. Figure 3.3 shows Dm for each created shape model, depending

Figure 3.1: Mean deviation of approximated position from ground truth depending on Q

13

3. Results and Discussion

Figure 3.2: Increase of deviation due to

Figure 3.3: Mahalanobis distance depending on Q

Figure 3.4: Change in estimated position (voxel), if landmark is known or not (Q = 9)

on the dimensionality. Dm = 3.5 seems to be sufficient as a constraint duringthe localization, if Q is ten or lower.

Figure 3.4 shows how much an estimated landmark position changes, if another landmark is not known either. As we can see, there is strong corre-lation between corresponding landmarks, especially between landmark oneand two (Mandibular nerve (V3)), landmark eight and nine (Processus sty-loideus) and landmark fourteen and fifteen (Ophthalmic nerve (V1)).

All in all, the shape model delivers an rough frame of the relations of the

14

3.2. Detection

landmark positions. It can provide location estimate with 10-20 voxel ac-curacy, if only others landmarks are known. The strongest relationships isbetween a landmark and its counterpart.

3.2 Detection

All three classifiers were tested with different number of negative samples.For the Bagged Trees classifier, it was determined, that a higher numberof negative samples improves the classification significantly. See figure 3.5.This contradicts a common rule in machine learning, that the accuracy de-creases with a too high number of negative samples (Hua et al. [2005]). Thisis not the case for the Subspace KNN classifier.

Depending on the landmark, a bigger descriptor is necessary. While land-marks Mandibular nerve (V3), Inferior alveoary nerve, Maxillary nerve (V2)and Ophthalmic nerve (V1) are detected with a descriptor with (5× 5× 5)the other landmarks are detected with a bigger descriptor more easily. Seefigure 3.6.

Although according to the confusion matrix, the Bagged Trees classifiershould be more precise, this does not seem to be the case. Figure 3.7 showsthe same cross section for both methods. If we look at the test area as ahole, the Subspace KNN test area has way more false positives in the upperand lower layers. In addition, the positive area around the ground truth isusually bigger, and therefore less exact.

Figure 3.5: Maximum probability for each x-, y-coordinate within test area of Mandibular nerve(V3) depending on number of negative samples. Classifier: Bagged Trees

15

3. Results and Discussion

Figure 3.6: Maximum probability for each x-,y-coordinate within test area of Spina nasalisanterior depending on descriptor size. Classifier Bagged Trees

Figure 3.7: Upper: Cross section Bagged Trees. Lower: Cross section Subspace KNN. Landmark:Mandibular nerve (V3)

16

3.3. Localization

Figure 3.8: Highest probability within 5 voxel of the ground truth per landmark.

Figure 3.9: Highest probability within a test area per landmark.

It is often the case, that a landmark is detected, with a lower probability, butnevertheless, it stands out of its environment. If the rest of the environmenthas an even lower probability, a detection is still possible. Figure 3.8 showsthe probability value distribution for each landmark. Figure 3.9 the highestvalue within each test area.

3.3 Localization

Figure 3.12 show the detection rate of the Bagged Trees gray value classifierper landmark. Blue is the detection rate, if just the maximal test value isassumed to be the landmark. Red is the solution of the iterative shape modelusage. Yellow is the use of the first shape model estimate. Violet stands fora distinguishing approach. When the maximal value is below a threshold of0.85 (see also 3.9), the iterative shape model solution is used, otherwise theimage maxima is used. Figure 3.13 shows the same data broken down to thesingle images.

Landmark 14, 17, 41 ad 48 were removed from the data set, due to probablewrong ground truth. There are three reasons, why s landmark has not beendetected. First, the rough estimate is too rough, and the ground truth isoutside the test area. Figure 3.10 gives an overview. Second, the landmarkhas been detected, but false positives lead to a wrong pick. In this case, it’s

17

3. Results and Discussion

Figure 3.10: Number of landmarks outside of test area by image.

Figure 3.11: Improvement of localization by shape model. Landmark: Mandibular nerve (V3).

the shape models turn. As shown in figure 3.11 this is can work quite well.The third case is wrong classification by the classifier (See figure 3.9.

The results (3.16 and 3.17) from using the SIFT3D descriptor in combinationwith the Bagged Trees classifier are worse for the landmarks that were de-tected quite well with the gray descriptor, but the result of landmark 10 and11 (Lateroorbital fissur ), as well as landmark 12 and 13 (Arcus zygomaticus)are better. Also the Sobel descriptor is generally less successfully then thegray value descriptor.

Due to more false positives and the delimitation of the ground truth to thesurrounding area, the detection of the images classified with Subspace KNNis dependent on the shape model. The results are generally worse and needmuch more computation (about 10 times longer). Not all 46 images wereevaluated for this report.

18

3.3. Localization

Figure 3.12: Detection rate gray value descriptor with Bagged Trees classifier by landmark. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method.

19

3. Results and Discussion

Figure 3.13: Detection rate of gray value descriptor with Bagged Trees classifier by image. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method.

20

3.3. Localization

Figure 3.14: Detection rate gray value descriptor with Bagged Trees classifier by landmark. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method.

21

3. Results and Discussion

Figure 3.15: Detection rate of Sobel value descriptor with Bagged Trees classifier by image. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method.

Figure 3.16: Detection rate of sift descriptor with Bagged Trees Classifier by landmark. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method.

22

3.3. Localization

Figure 3.17: Detection rate of sift descriptor with Bagged Trees Classifier by image. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method.

Figure 3.18: Detection rate of gray descriptor with Subspace KNN classifier by landmark. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method. 29Images were tested.

23

3. Results and Discussion

Figure 3.19: Detection rate of SIFT descriptor with Subspace KNN classifier by landmark. Blue:Maximum value. Red: Iterative solution. Yellow: Initialization. Violet: Threshold method. 13images were tested.

24

Chapter 4

Conclusion

Depending on the quality of the image and type of landmark, detectionwithin cone beam computer tomography-images by using standard ensem-ble classifier is possible.

A practical application of such a pipeline would be the support of medicalprofessionals in their daily work life. The classifiers could be continuouslytrained and the professional could be informed if a landmark is not found,it might indicate an abnormality.

The use of a shape model can help, especially with landmarks that are notalways properly detected by the classifier (Arcus zygomaticus, Ophthalmicnerve (V1)) and when the accuracy requirements are not too high. Furtherimprovement of a well detected landmark to sub voxel quality is hardlypossible.

Additional work can certainly be done in the beginning. Especially the re-duction of the test area would help to increase speed and reduce possibilitiesof false positives. It might be a good idea to fist evaluate well recognizablelandmarks, and use their position to reduce the test area of the other land-marks. The iterative use of the shape model could be linearized for increasedspeed according to (Cootes et al. [1994]).

Also the technical characteristics of the cone beam computer tomographysystem (Scarfe and Farman [2008]) and its influence on the shape modelcould be analyzed. For example if there are distortions depending on thesize of the head.

25

Bibliography

Timothy F Cootes and Christopher J Taylor. Active shape models—‘smartsnakes’. In BMVC92, pages 266–275. Springer, 1992.

Timothy F Cootes, Andrew Hill, Christopher J Taylor, and Jane Haslam. Useof active shape models for locating structures in medical images. Imageand vision computing, 12(6):355–365, 1994.

Jianping Hua, Zixiang Xiong, James Lowey, Edward Suh, and Edward R.Dougherty. Optimal number of features as a function of sample sizefor various classification rules. Bioinformatics, 21(8):1509–1515, 2005.doi: 10.1093/bioinformatics/bti171. URL http://dx.doi.org/10.1093/

bioinformatics/bti171.

Rich Radke. Intro to digital image processing, November 2015.

B. Rister, M. A. Horowitz, and D. L. Rubin. Volumetric image registrationfrom invariant keypoints. IEEE Transactions on Image Processing, 26(10):4900–4910, Oct 2017. ISSN 1057-7149. doi: 10.1109/TIP.2017.2722689. URLhttps://github.com/bbrister/SIFT3D.

William C Scarfe and Allan G Farman. What is cone-beam ct and how doesit work? Dental Clinics, 52(4):707–730, 2008.

27

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