Global Hybrid Registration for 3D Constructed Surfaces using

Ray-casting and Improved Self Adaptive Differential Evolution

Algorithm

Tao Ngoc Linh

1

, Tam Bui

1

and Hasegawa Hiroshi

2

1

Deparment of Functional Control Systems, Graduate School of Engineering and Science,

Shibaura Institute of Technology, Saitama 337-8570, Japan

2

Department of Machinery and Control System, College of Systems Engineering and Science,

Shibaura Institute of Technology, Saitama 337-8570, Japan

Keywords:

3D Registration, ISADE, Global Registration, Ray-casting.

Abstract:

As a fundamental task in computer vision, registration has been a solution for many application such as:

world modeling, part inspection and manufacturing, object recognition, pose estimation, robotic navigation,

and reverse engineering. Given two images, the aim is to ﬁnd the best possible homogenous transformation

movement resulting in a more completed view of objects or scenarios. The paper presents a novel algorithm

of registering structured pointcloud surfaces by using a fast ray-casting based closest point method intergrated

with a new developed global optimization method Improve Self Adaptive Differential Evolution (ISADE).

Ray-casting based L

2

error calculation method enables the algorithm to ﬁnd the local minima error effectively

while ISADE exploits the searching boundary to ﬁnd the global minima. The new algorithm is evaluated on

structured images captured by a Kinect camera to show the superior in quality and robustness of ISADE over

state-of-the-art searching method and accuracy of the new method over a well known registration algorithm,

KinectFusion.

1 INTRODUCTION

The introduction of commercial depth sensing devices

such as Microsoft Kinect, Asus Xtion, etc has shifted

robotics, computer vision research areas from 2D

based imaging and laser scanning toward 3D based

depth scenes of environment processing. As a physi-

cal object or scenario can not be completely captured

with a single image, different images from different

time and positions need to be aligned into a more

completed view of the senario, the process of align-

ment is called registration. Registration algorithms

estimate the movement of the camera through cal-

culating the transformation that optimally maps two

point clouds. Various applications such as 3D ob-

ject scanning, 3D mapping, 3D localization use reg-

istration algorithms as backbone algorithms. Accord-

ing to how many views or images of the objects are

processed at the same time, registration strategies

are divided into multi-view registration (for all views

case) and pair-wise registration (for two views case).

Our paper focus on the pair-wise registration of con-

structed range images taken by 3D cameras. As a con-

sequence, starting from two views, i.e., the model and

the data, the objective of our registration process is to

ﬁnd the best homogeneous transformation that, when

applied to the data, aligns it with the model in a com-

mon coordinate system.

Iterative Closest Point (ICP)(1) and its variants

such as non-linear ICP, generalized ICP and non-rigid

ICP have been always indispensable tools in registra-

tion tasks. ICP’s concept and implementationare easy

to understand. ICP uses L

2

error estimated from pair-

wise point-clouds to derive a transformation which

draws them closer to each other. Registration process

ﬁnishes after many iterations of minimizing error and

results in a homogeneous transformation.

However, ICP-class algorithms alone cannot solve

problems for general registration tasks since they re-

quire a further assumption in which a initial near-

optimal pose transformation is necessary for right

convergences. Otherwise, the registration process

would likely converge to local optimal solutions in-

stead of the global optimal or near global optimal

one. This result cannot be overcome merely by it-

eration procedure. In some mesh and point-cloud edi-

Linh, T., Hiroshi, H. and Bui, T.

Global Hybrid Registration for 3D Constructed Surfaces using Ray-casting and Improved Self Adaptive Differential Evolution Algorithm.

DOI: 10.5220/0005718901670174

In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2016) - Volume 4: VISAPP, pages 167-174

ISBN: 978-989-758-175-5

Copyright

c

2016 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

167

tor softwares such as Meshlab (2), registering tool for

range data is available. It requires manually data pre-

alignment from users before ICP comes into use.

To overcome the shortage of ICP-class methods,

in general, registration processes are generally di-

vided into two steps: coarse transformation or initial-

ization and ﬁne transformation. If two point-clouds

are close enough, the ﬁrst step could be omitted. Oth-

erwise, the problem remains a big challenge for re-

searchers. Coarse transformation, pre-alignment es-

timation or initialization solving has two approaches:

local and global. Local methods use local descriptors

(or signatures) such as PFH(3) and SIFT(4) which en-

code local shape variation in neighborhood points. If

points with those descriptors appear in both register-

ing point-clouds, initialization movement could be es-

timated by using sample consensus algorithms such

as RANSAC (5). The problem of local approaches is

that those signatures are not always guarantied to ap-

pear on both registering point-clouds. On the other

hand, global approaches take every points into ac-

count such as Go-ICP (6) and SAICP(7). The biggest

problem of those methods is computation cost in ﬁnd-

ing the corresponding points in point-clouds. If there

are big number of point in point-clouds, the compu-

tation cost is going large. However, thanks to new al-

gorithms especially heuristic optimal searching meth-

ods as well as the increasing in computer speed espe-

cially with parallel computing with multi-core CPU

processor and Graphic Computation Unit (GPU)(8) it

is possible to ﬁnd solutions of global approaches of

registration problem. After estimating coarse trans-

formation, ICP algorithm is an efﬁcient tool to ﬁnd

the ﬁne transformation.

This paper proposes a new global registration

method for 3D constructed images without need of

good initializing. It is called Global Hybrid Registra-

tion for 3D Constructed Surface Using Ray-casting

and ISADE (12). As other global registration meth-

ods, our method requires no local descriptors on

works directly on raw scan surfaces. The method uses

ray-casting based method for local minima searching

together with ISADE as a search engine to ﬁnd the

global minima without using ﬁne registration. Our

method rapidly produces results at high rate conver-

gence of the global optimization solution.

2 THREE DIMENSION

REGISTRATION

This part summaries some approaches for global

range image registration task up to date. SVD, PCA

(13) are integrated together with ICP as classical

methods and global searching algorithms are inte-

grated with ICP as in the most current methods.

2.1 ICP Algorithm

SVD and PCA have been used to ﬁnd coarse trans-

formation together with ICP as the ﬁne transforma-

tion estimating tool. Original version of ICP algo-

rithm relies on L

2

error to derive the transforma-

tion including rotation and translation. To register

two point-clouds X = {x

i

},{i = 1, 2,3,...,m} (model

point-cloud) and Y = {y

j

},{ j = 1,2,3,..., n} (data

point-clouds), where x

i

and y

j

∈ R

3

are point coor-

dinates of points in point-cloud. ICP algorithm arms

to ﬁnd rotation R ∈ SO

3

and translation t ∈ R

3

, which

minimize L

2

type error as in Equation 1:

E(R,t) =

n

∑

i=1

e

i

(R,t) =

n

∑

i=1

|Rx

i

+ t− y

j

∗

| (1)

where R and t are rotation and translation matrix, y

j

∗

is the corresponding point of x

i

denoted for its clos-

est point in data point-cloud Y. There are some ICP

variants which rely on different categories to deﬁne

closest points. Point-to-point and Point-to-plane are

two popular examples. Equation 2 is used to search

for closest point by Point-to-point category.

j

∗

= argmin

j∈{1,...,n}

||Rx

i

+ t− y

j

|| (2)

The iteration process is as following to archives the

ﬁnal transformation:

1. Compute the closest model points for each data

point as (2).

2. Compute the transformation R and t based on

the error from (1).

3. Apply R and t to the data point-clouds.

4. Repeat step 1, 2, 3 until error as (1) smaller

then a set tolerant or the procedure reaches its max

iteration.

Step by step, ICP draws the data point-cloud

closer to model point-cloud and the process stops

at local minima. There are some variants of ICP

algorithm based on different methods to calculate the

transformation from error E(R,t) and error itself as

in LMICP (14) and SICP (15).

2.2 Global Hybrid Searching Algorithm

ICP algorithms are superior for registering close or

pre-aligned point-cloud data, otherwise, it often con-

verges wrongly. Global searching algorithms are so-

lution to solve this problem since they are able to ﬁnd

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

168

ICP step

ICP to local best

Begin p osition

Local best

Local best

NA search jump

Global best

Figure 1: global searching algorithm with ICP integrated.

f(x)

x

Figure 2: Example of ﬂatten objective function after icp in

red color where original function is in black.

the global minima instead of local one. To make the

task of global searching algorithm less difﬁcult, ICP

are often applied to ﬂatten the searching space. Fig-

ure 1 and Figure 2 show how ICP works as a objec-

tive function ﬂattening tool. By using ICP, a complex

ﬁtness function in black turns into simpler one in red

color. And with such a much more ﬂatten ﬁtness func-

tion, global searching method ﬁnd a global minima

more effectively.

The integration work well in case of point-cloud

data with small point number. For large data case,

ICP becomes slow and impossible for applying into

real time applications. Our method integrates new

global searching algorithm ISADE which works well

in complicated ﬁtness function without ﬂattening pro-

cess and fast error calculation method based on ray-

casting corresponding searching algorithm which ac-

celerates registration procedure to high speed.

3 METHOD OVERVIEW

3.1 Methodology Approach

The biggest disadvantage of ICP based registration

methods in calculating cost function is runtime. In

KinectFusion (16), a real-time scene reconstruction

algorithm, ICP is used as a only method for regis-

tering two continuous frames. The method requires

a powerful Graphic Card to fasten calculations and

reduce runtime. However, in global registration algo-

rithms with thousand times of error function calcula-

tion more than ICP through many iterations and pop-

ulations, to make the algorithm can run real-time, we

need a faster error calculation method. The proposed

algorithm takes the advantage of fast error calculat-

ing by using ray-casting based corresponding point

searching to applied for a new optimization algorithm

ISADE with a purpose of getting a faster and global

optimal convergence guaranty.

3.2 Ray-casting Closest Point

ICP-class algorithms often uses kd-tree(17) structure

to speed up the process of ﬁnding j

∗

in Equation 2.

The order of kd-tree searching closest algorithm is

O(log(n)) where n is number of searching point set.

Figure 3 shows an example of corresponding points

of the data point-cloud in the model one.

Figure 3: closest corresponding point deﬁned in original

ICP algorithm.

Since depth image or point cloud data are often

obtained from 3D range camera in which the data

could be consider as an 2D gray image G where value

of each pixel show the depth of the point.

z

i,j

= G

i,j

(3)

where z

i, j

is depth of image at pixel i,j.

Equations 4 is to convert from depth image and real

3D depth data {x,y,z}.

x

i,j

= (i− cx)G

i,j

/fx (4a)

y

i,j

= (j− cy)G

i,j

/fy (4b)

z

i,j

= G

i,j

(4c)

where fx, fy, cx, cy are intrinsics of the depth camera.

In conversion, pixel position and structured expres-

sion of a point x,y,z can be calculated as equation 5.

G

i,j

= z

i,j

(5a)

i = round(cx+ x

i,j

∗ fx/G

i,j

) (5b)

Global Hybrid Registration for 3D Constructed Surfaces using Ray-casting and Improved Self Adaptive Differential Evolution Algorithm

169

j = round(cy+ y

i,j

∗ fy/G

i,j

) (5c)

Equations 5 is to calculate i,j of data points which are

also i,j of corresponding point in model point-clouds.

The idea of the method is showed as Figure 4 which

reminds the ray-casting process in computer vision.

j

i

datamodel

camera origin

Figure 4: Ray-casting method for searching corresponding

point.

3.3 Objective Function

The ﬁtness function need to provide an error score

that is minimized when the best transformation ma-

trix are applied. The paper uses ﬁtness function as

Equation 6.

F(R,t) = f(n)

1

n

2

n

∑

i=1

(Rx

i

+ t− y

j

∗

)

2

(6)

where f(n) is a function of inlier point number, n,

dependence. n is the number of inlier points in the

data point-cloud.

The error function should be smaller in bigger number

of inlier point. Since that, searching algorithm would

get rid of the case in which cost function is small for

only small inlier points. Function f(n) is calculated

as in Equation 7.

f(n) =

∞

1− n/N

if

n < N/10

n > N/10

(7)

where N is number of points in the data point-cloud.

3.4 ISADE

Differential evolution (DE) is an optimization tech-

nique originally proposed by Storn and Price (18). It

is categorized into evolution algorithm group which is

characterized by operators of mutation and crossover.

In DE, two important coefﬁcients which play key rolls

to decide the correction and speed of convergence are

scaling factor F and crossover rate C

r

. Another im-

portant parameter in DE, population size NP remains

a user-assigned value to cope with problem com-

plexity. ISADE not only adaptively changes those

three coefﬁcients but also integrates different muta-

tion schemes to take advantages of them.

3.4.1 Adaptive Learning Strategies Selection

In their paper of ISADE, Tam Bui et al. ran-

domly chose three mutation schemes which

are DE/best/1/bin, DE/best/2/bin and

DE/randtobest/1/bin. Among DE’s schemes,

DE/best/1/bin and DE/best/2/bin are known

for good convergence property and ”DE/rand to

best/1/bin” is known for good diversity. The

probability of applying those strategies are equal

equally assigned at with values p

1

= p

2

= p

3

= 1/3.

Equations 8 show the formula of chosen schemes.

DE/best/1 : V

G

i, j

= X

G

best, j

+ F(X

G

r1, j

− X

G

r2, j

) (8a)

DE/best/2 : V

G

i, j

= X

G

best, j

+ F(X

G

r1, j

− X

G

r2, j

)

+ F(X

G

r3, j

− X

G

r4, j

) (8b)

DE/randtobest/1 :V

G

i, j

= X

G

best, j

+F(X

G

best, j

−X

G

r2, j

)

+ F(X

G

r2, j

− X

G

r3, j

) (8c)

3.4.2 Adaptive Scaling Factor

In APGA/VNC appoach proposed by S.Tooyama and

H.Hasegawa (19), scaling factor changes according to

iteration as sigmoid function as in Equation 9.

F

i

=

1

1+ exp(α∗

i−NP/2

NP

)

(9)

ISADE give addition scaling F

mean

i

as in Equation 10.

F

mean

i

= F

min

+ (F

max

− F

min

)(

i

max

− i

i

max

)

n

iter

(10)

where

n

iter

= n

min

+ (n

max

− n

min

)(

i

i

max

) (11)

F

i

in Equation 9 is modiﬁed as in Equation 12.

F

i

=

F

i

+ F

mean

i

2

(12)

Now scaling factor is set to be high in ﬁrst iterations

and after certain generations it become smaller for

proper exploitation.

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

170

3.4.3 Crossver Control Parameter

ISADE algorithm is able to detect whether hight val-

ues of C

r

are useful and if a rotationally invariant

crossover is required. A minimum base for C

r

around

its median value is incorporated to avoid stagnation

around a single value. The control parameter C

r

is

assigned as Equation 13.

C

i+1

r

=

rand

2

ifrand

1

6 τ

C

i

r

otherwise

(13)

where rand

1

and rand

2

are random values ∈ [0,1], τ

presents probability to adjust C

r

. C

r

is adjusted as in

Equation 14.

C

i

r

=

C

r

min

C

r

min

6 C

i+1

r

6 C

r

medium

C

r

max

C

r

medium

6 C

i+1

r

6 C

r

max

(14)

where C

r

min

, C

r

medium

, C

r

max

denote low value, median

value and high value of crossover parameter respec-

tively. As in (12), we take τ = 0.1, C

r

min

= 0.05,

C

r

medium

= 0.50, C

r

max

= 0.95.

All above ideas and theories are implemented as in

ﬂowchart in Figure 5.

Population Initialization

Start

Population rank evaluation

Adaptive scaling factor F

i

parameter C

r

Adaptive crossover control

Mutation with learning with

diﬀerent strategies

Crossover

Selection

Ranking ﬁnd best so far

maxgen?

Stop

No

Yes

Figure 5: ISADE implementation process.

3.5 A New Combination Method

From initial position matrix, using ICP with one it-

eration to gain a slightly better rotation and transla-

tion matrix. The algorithm recalculates the error as in

Equation 6 and uses it in ISADE searching algorithm.

Flowchart in Figure 6 shows implementation of the

whole algorithm.

Generate new set of movement

Start

Calculate optimized Rotation a nd

Calculate cost function for each

Mutation, crossover, selectio n from ISADE

Ranking ﬁnd best so far

maxgen?

Stop

No

Yes

Translation matrix for each position

new rotation and translation matrix

Figure 6: Registration with ISADE and Ray-casting.

4 EXPERIMENT AND RESULTS

This section arms at presenting a number of exper-

imental results to study how robust and accurate of

ISADE results in comparison to other Global search-

ing algorithm in using the same ray-casting based

error function as well as comparison of result from

new algorithm to KinecFusion in term of accuracy.

1) De Falco et al’s proposal (DE), Differential

Evolution as a viable tool for satellite image registra-

tion (20).

2) Valsecchi et al.’s proposal (GA), An Image

Registration Approach using Genetic Algorithms

(11).

3) Talbi et al.’s proposal (PSO), Particle Swarm

Optimization for Image Processing (10).

4) Luck et al.’s proposal (SA), registration of

range data using a hybrid simulated annealing and

iterative closest point algorithm (7).

The proposed algorithm is implemented in C++ and

compiled with GNU/g++ tool.

In order to perform a fair comparison between dif-

ferent optimization tools, in all methods, maximum

iteration is set to 100 with population of 25 for each

iteration. As SAICP is not a multi agent methods, its

maximum iteration is set to 2500.

4.1 Range Image Dataset

Our experiments carry out number of pair-wise

Global Hybrid Registration for 3D Constructed Surfaces using Ray-casting and Improved Self Adaptive Differential Evolution Algorithm

171

Figure 7: RGB-D 7 scenes Dataset for experiments.

registration task using well-known Depth data

taken from Kinect Microsoft Camera down-

loaded from website of Microsoft Research

http://research.microsoft.com/en-us/projects/7-

scenes/. Speciﬁcally, Figure 7 shows all scenes:

Chess, Fire, Heads, Ofﬁce, Pumpkin, RedKitchen,

Stairs.

Those png format depth images are sub-sampled

into smaller solution of 128 × 96 which is 5 times

smaller than original solution of 640 × 480 in each

dimension. The reason for using smaller number of

points dataset is to archive considerable suitable run-

time while accuracy remains unchanged.

4.2 KinectFusion Error from Camera

Transpose

Accompany with depth datasets, 7 scenes database

gives us camera homogeneous transposes at each

frame calculated from Kinect-Fusion algorithm. Us-

ing those transpose, we could calculate transforma-

tion matrix between two scene as Equations 15.

T

j

i

= T

−1

i

∗ T

j

(15a)

T

j

i

=

R

j

i

t

j

i

0 0 0 1

(15b)

where T

j

i

is transformation matrix to move frame j to

align with frame i, T

i

and T

j

are homogeneous trans-

pose matrix for camera at frame i and j respectively,

R

j

i

,t

j

i

are rotation and translation matrix of T

j

i

.

R

j

i

,t

j

i

are applied into ray-casting error calculation

methods for two frames as in Equation 6 to draw er-

rors of KinectFusion algorithm for the next compari-

son step.

4.3 Parameter Settings

In each methods 30 runs were executed with two reg-

istration depth images are at distance of 20 frames

in the sequence. The searching space is set so rota-

tion and translation limitation at [−2π/10,2π/10] and

[−0.3, 0.3] separately. All methods are run on a PC of

Intel core I7-4790 CPU 3.60 GHz × 8 processor and

8 GB of RAM memory.

4.4 Comparision between Different

Algorithms

ISADE searching algorithm results are compared

with other algorithms’ results in three categories in-

cluding convergent rate, mean and standard deviation

which are shown in Table 1.

Table 1: Results of different algorithms for 7 scenes.

Scene name Algorithm CvR (%) Mean St. dev.

Chess ISADE 100 0.0695 0.0107

ref: 0.2483 DE 100 0.0752 0.0144

GA 0 1.8018 0.6643

PSO 10 0.6753 0.4502

SA 6.6667 0.9413 0.7171

Fire ISADE 100 0.0230 8.8565e-04

ref: 0.2431 DE 100 0.0290 2.5576e-04

GA 0 0.7740 0.2300

PSO 20 0.3497 0.2826

SA 6.6667 0.3306 0.2679

Heads ISADE 100 0.0024 3.5903e-05

ref: 2.9907 DE 100 0.0027 0.0048

GA 100 0.3080 0.1349

PSO 100 0.0824 0.0836

SA 73.3333 0.4494 0.3385

Ofﬁce ISADE 100 0.0358 8.4689e-05

ref: 0.6294 DE 100 0.0371 8.2449e-04

GA 100 0.8577 0.3445

PSO 100 0.2819 0.3702

SA 33.3333 0.5526 0.5851

Pumpkin ISADE 100 0.0407 0.0071

ref: 0.111361 DE 100 0.0489 0.0127

GA 0 1.1097 0.4057

PSO 6.6667 0.3779 0.3330

SA 0 6.6667 0.6984

RedKitchen ISADE 100 0.0315 0.0049

ref: 0.0984 DE 93.3333 0.0473 0.0239

GA 0 1.4215 0.6508

PSO 0 0.4863 0.3829

SA 10 0.3021 0.2898

Stairs ISADE 100 0.0056 5.6268e-06

ref: 0.0156 DE 100 0.0062 0.0014

GA 0 0.9413 0.3373

PSO 0 0.2441 0.2435

SA 3.3333 0.4808 0.6281

KinectFusion error or reference value is considered

as correct convergence. In Table 1, convergence rate

(CvR) means percentage of algorithms results smaller

than reference value.

Proposed algorithm and DE are superior than

other methods in every categories. ISADE are bet-

ter than DE in almost cases only in the Fire scene

standard deviation of ISADE method larger than DE

method’s.

The proposed method are qualiﬁed in all tested

scenes with convergence value are always smaller

than reference value. This can be explained by ac-

cumulating error by using ICP algorithm from frame

to frame. As using ICP continuously from frame to

frame in Kinect Fusion algorithm error would be ac-

cumulated and become large. The ﬁnal transforma-

VISAPP 2016 - International Conference on Computer Vision Theory and Applications

172

tion matrix becomes less accurate than which gained

from direct registration method using only two frame.

Figure 8 shows four scenes registration results

using ISADE integrated algorithms including: Fire,

Head, Ofﬁce, Stairs. Model pointsets are in red and

data pointsets are in grey color.

4.5 Runtime

For the data of 128× 96 resolution, average running

time for the proposed method are shown in Table 2.

The results show the average time for registration at

Table 2: Average runtime (in second) on different scenes.

Chess Fire Heads Ofﬁce Pumpkin RedKitchen Stairs

7.5053 5.8596 8.0114 7.4527 5.9005 6.0466 7.8627

around 8 second. Two registering frames are at dis-

tance of 20 frames. That means the rate of register-

ing equivalence at rate of 2.5 fps (frames per second).

To make algorithm run at real-time rate of 20fps, the

speed need to be increased by 8 times. This is pos-

sible if we exploit all core of 8-core-processors not

mention using GPU.

Figure 8: Registration output example.

5 DISCUSSION AND

CONCLUSION

Image registration has been a very active research

area. Recently, the approach of using evolutionary

algorithms (EAs), especially new methods, proved

their potential of tackling image registration problem

based on their robustness and accuracy on searching

for global optimal. With EAs algorithm as search-

ing tools, it is not necessary to have good initials to

avoid local minima and converge to near-global min-

ima solutions. To do that, EAs algorithms need tuning

carefully to gain best results.

We proposed the new registration algorithm by in-

tegrating a new self-adaptive optimization algorithm

(ISADE) into a fast closest point searching method to

tackle well-known challenging task of computer vi-

sion area. In the experiments, the results show that

ISADE is able to ﬁnd a robust and accurate transfor-

mation matrix of camera movement.

What is more important, accuracy and robustness

results has been obtained in comparison with other

state-of-the-art evolution based algorithms. ISADE

shows its superior than GA, PSO, SA in searching

for global minima solution. In comparision with

DE, ISADE also show its much better in almost

tested scenes. The robustness and accuracy is tested

and proved in real 3D scenes captured by Microsoft

Kinect camera.

In term of running time, by using fast searching

closest point methods, proposed algorithms are con-

sidered fast in our sense. It shows potential of apply-

ing in real-time application if using parallel program-

ing technique with multi-core processors.

In future work, ISADE algorithm can be imple-

mented in parallel in GPU (Graphic Processor Unit)

which can help algorithm reduces runtime to prove

real-time implement possibility in 3D reconstruction,

3D mapping and 3D localization.

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