Comparative Study of Depth-Image Matching with Steepest

Descendent and Simulated Annealing Algorithms

Hiroshi Noborio, Shogo Yoshida, Kaoru Watanabe, Daiki Yano and Masanao Koeda

Department of Computer Science, Osaka Electro-Communication University, Shijo-Nawate, Japan

Keywords: Simulated Annealing, Steepest Descendent, Organ-following Algorithm, Depth-Depth Matching.

Abstract: We have been developing a depth-depth matching-based organ-following algorithm for use in surgical

navigation. In this paper, we experimentally compare the steepest descendent and simulated annealing

algorithms under depth-depth matching. Our experiment can be performed in a real-life situation like practical

surgery as follows: the organ is artificially occluded by another object corresponding to a human body, and

surgery is performed on a real surgical bed beside two shadow-less lamps. In this research, in addition to the

algorithm comparison, we checked the effect of the placement of two infrared shielding filters, SL999 and

TS6080S. Based on the results, we could determine that the simulated annealing algorithm using the filter

TS6080S is the best.

1 INTRODUCTION

Many types of surgical navigation systems have been

developed in commercial and research fields. Nearly

all systems in the commercial field can be seen at the

"Medical expo" website (http://www.

medicalexpo.com/). Several surgical navigation

systems have been investigated in the research field

as well.

However, the intended targets of such systems are

the brain (Ferroli, 2013; Schulz, 2012) or the bone

(Blakeney 2011; Schnurr 2011). In almost all

navigation researches, the bone is completely fixed

by plastic components and consequently is not

deformed. In addition, the brain is almost entirely

confined by the skull and is not deformable except

when considering the well-known case of brain shift.

Therefore, the shape, position, and orientation of the

brain and its inner parts such as several kinds of

tumours, blood vessels, and nerves are precisely

calculated.

Therefore, conventional surgical navigations

systems do not consider large rotations/translations or

deformations in the targeted systems. For this reason,

we focus on the organ-following algorithm that

considers the deformation by using a liver with

arteries, veins, portal veins, and tumor, or brain with

a shift, and so on (Noborio, 2013; Noborio, 2016a;

Noborio 2016b). We compared several kinds of depth

cameras such as RICOH SV-M-S1, SICK V3310,

Microsoft Kinect v1 and v2, Intel RealSense, and

Euclid to get the deformation (the surface depth

image) of the liver and brain during a real-time

surgery. In this paper, we focused on following a real

organ and scalpel cavitron ultrasonic surgical

aspirator (CUSA) by its virtual organ and scalpel

CUSA after calibrating both coordinate systems. Our

previous papers addressed this agenda realistically by

attaching some cameras directly besides a surgical

bed in a real surgical room with two shadow-less

lamps covered by two types of infrared filters. In this

paper, while maintaining this realistic set-up, we

experimentally compare two types of search

algorithms—steepest descendent and simulation

annealing. In addition, during the comparison, we

tested the effect of placing two infrared shielding

filters SL999 and TS6080S around the two shadow-

less lamps. The results showed that the combination

of simulation annealing and the infrared filter

TS6080S is the best for following a real liver by its

virtual liver in a real surgical room with two shadow-

less lamps.

In section 2, we describe the real and virtual livers

used in our experiment, and then explain our key idea

of depth-image matching. In section 3, we first show

our surgical room for an obstructed liver, which is

equipped with two shadow-less lamps. Then, we

compare the steepest descendent and simulated

Noborio, H., Yoshida, S., Watanabe, K., Yano, D. and Koeda, M.

Comparative Study of Depth-Image Matching with Steepest Descendent and Simulated Annealing Algorithms.

DOI: 10.5220/0006644200770087

In Proceedings of the 11th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2018) - Volume 1: BIODEVICES, pages 77-87

ISBN: 978-989-758-277-6

annealing algorithms. Finally, in section 4, we present

some concluding remarks.

2 DEPTH-IMAGE MATCHING

AND OVERLAPPING RATIO

BETWEEN REAL AND

VIRTUAL LIVERS

From 2014, we have been developing several kinds of

organ-following algorithms based on the steepest

descendent algorithm from a virtual world simulation

(Noborio, 2014a) to a real world experiment

(Noborio, 2015a). In addition, we tested these

algorithms in an experimental room and an actual

surgical room with zero, one, and two shadow-less

lamps. Moreover, we checked the usefulness of

placing infrared shielding filters, SL999 and

TS6080S (Noborio, 2017), on the lamp. Then, we

recently compared the classic steepest descendent

algorithm and the new simulated annealing algorithm

in an actual surgical room with two shadow-less

lamps enclosed by one of the two infrared filters,

SL999 and TS6080S.

Figure 1: (a) Polyhedral liver in stereolithography STL

format, (b) its 3D-printed plastic template, and (c) plastic

liver pushed in the template.

In this chapter, we briefly explain our depth-depth

matching method used in two kinds of search

algorithms. The function value generated by the

depth-depth matching is used for the evaluation index

of the search algorithm. Then, we explain in detail the

steepest descendent and simulated annealing

algorithms. The steepest descendent algorithm does

not have a function for escaping from several local

minima. Therefore, it sometimes overlooks the

position/orientation where a virtual organ is

coincident with the real organ. To overcome this, we

prepared two kinds of randomized functions

(Noborio, 2016c). Contrary to this, the simulated

annealing algorithm includes the escaping function.

Therefore, we do not need to prepare such a function

additionally, which is an advantage.

Figure 2: Position/orientation of the virtual liver model is

analyzed to decrease the difference in its depth images and

that of the actual liver.

2.1 Fast Depth-Depth Matching

The most important function in our surgical

navigation is to track a virtual liver model (which is

displayed to users) against a real liver, and to match

the positions/orientations of the two liver samples at

any time (Figure 1).

In our research, a depth camera such as the Kinect

v2 captures the surface depth image of an organ.

Simultaneously, the graphics processing unit (GPU)

BIODEVICES 2018 - 11th International Conference on Biomedical Electronics and Devices

board on the PC generates the surface depth image of

the 3D virtual organ model. In Figure 2, we use the

depth-image matching between the real and virtual

worlds, whose positions and orientations were

completely calibrated in advance.

Figure 3: (a), (b) Search spaces containing 12 and 728

neighbouring candidates with six DOF space. (c),(d) Search

spaces containing 52 and 248 neighbouring candidates with

three translational DOF and three rotational DOF.

Each of the two kinds of proposed algorithms will

always seek a better positon/orientation of the virtual

liver against the positon/orientation of the real liver.

By shifting slightly each time within the six degrees-

of-freedom (DOF) space by (x, y, z, φ, θ, ψ), where

x, y, z are the coordinates in the Euclidean 3D space,

φ is the roll angle, θ is the pitch, and ψ is the yaw

(Figure 3), we can find a better neighbouring point

(positon/orientation) of the virtual liver whose

overlapping ratio is minimum, as explained later. As

mentioned in (Watanabe, 2015), searching the 6D

digitalized space is quite time consuming. For this

reason, we attempted to divide the 6D space into a 3D

translation space and a 3D rotation space whose

difference was changed from 1 to 3.

To obtain a function value (=overlapping ratio)

using our search algorithm, it is better to match the

real and virtual depth images for matching the real

and virtual 3D point clouds (Liu, 2006; Wu, 2015).

The reason is as follows:

(1) The number of pixel depths is quite less than the

number of points (Figure 4).

(2) The former needs the sum of non-combinational

distance differences (e.g., for 1024*1024 pixels)

but the latter requires the sum of combinatorial

shortest distance calculations (e.g., for

combination pairs between one million or more

points in some point cloud) (Liu, 2006; Wu,

2015).

Figure 4: Summed differences between the real and virtual

depth images based on pixels selected randomly in parallel

on the GPU.

2.2 Randomized Algorithm based on

Steepest Descendent

Using a selected search algorithm, we can match the

positions and orientations of the virtual liver model

and the real liver. As mentioned, we tested two kinds

of randomized algorithms in order to decrease the

differences between the depth images of the virtual

and real liver models.

First, we designed a randomized algorithm based

on steepest descendent (Figure 5), which is used in a

real surgical room with an infrared filter, (Noborio,

2017) as follows:

Comparative Study of Depth-Image Matching with Steepest Descendent and Simulated Annealing Algorithms

Figure 5: Flowchart illustrating depth-depth matching in

our randomized algorithm, based on the steepest descendent

method.

Given an initial guess x

, the method always

computes a sequence of iterates x

among six-

dimensional digitalized space (three are the

translational degrees-of-freedom and the other

three are the rotational degrees-of-freedom).

At x

, the algorithm always selects a neighbor

whose randomized value f is minimized from

many digitalized neighbors whose distances are

1 and 2 as x

k+1

, as shown in Figure 3.

Figure 6: We randomly select a group of N pixels from each

image. Then, we calculate the minimum, median, or

average of the difference distribution between the real and

virtual depth images. Furthermore, we select the minimum,

median, or average of the evaluation values in M images.

Their randomizations escape from a local minimum in the

motion space in our steepest descendent.

In this algorithm, in order to escape from several

local minima in the search space, we use two kinds of

randomizations (Figure 6).

(1) For each image, M pixels are randomly selected,

and the minimum, median, or average of their

differences are calculated.

(2) For N images, we select their minimum, median,

or average calculated in (1) as the evaluation value

for the search.

(3) In (1) and (2), we set M and N to 10, 50, and 100,

respectively. This parameter selection is

important for each organ.

2.3 Simulated Annealing Algorithm

In this section, we explain our simulated annealing

algorithm as another type of randomized algorithm

(Watanabe, 2017). Simulated annealing (SA) was

first proposed in 1983 by Kirkpatrick et al.

(Kirkpatrick, 1983). It was fortunately rediscovered

in 1985 by Vlado Cerny (Cerny, 1985). SA is a

metaheuristic that finds global optimization in a large

search space. Steepest descent is a simple search

method. At each step, it selects the best neighbor of

the current point that is stuck at a local optimum and

often cannot find a global optimum. SA selects a

neighbor probabilistically and finds the global

optimum for a sufficiently long time.

A_search(ti)

t ← ti

p ← position/orientation of the virtual liver

model at time ti

f ←fitness (p)

f_best ← f

p_best ← p

while (t i+1 － t > 0)

randomly select a neighbor p’ of p such

that |p’i － pi | ≦ D for all i

f ' ← fitness(p’)

if f' < f_best then

f_best ← f '

p_best ← p’

if f' < f or

random(0,1) ≧ (t － ti) / Δt then

f_best ← f '

p_best ← p’

t ← t+1

BIODEVICES 2018 - 11th International Conference on Biomedical Electronics and Devices

Figure 7: A 2D virtual liver, whose pixel is depicted in blue,

is starting to overlap with its 2D real liver, whose pixel is

depicted in red, in the depth image. In our matching system,

the overlapping area in the XY plane is described by a set

of yellow pixels, and the overlapping area in the XYZ space

is described by a set of blue pixels.

The random function (0,1) returns a random value

from zero to one. The fitness (p’) in this algorithm

equals the randomized value f of the steepest

descendent and it indicates the difference between the

two depth images. The parameter D is half the width

of the area, which is a six-dimensional hypercube

with width 2D, in which a new position/orientation p’

is randomly generated. If D increases, the algorithm

can choose a more distant neighbor to avoid falling

into a local minimum.

In this algorithm, f' < f_best implies that we obtain

the global minimum and f' < f implies that we obtain

the local minimum. To escape from the local

minimum, we prepare random (0,1) ≧ (t−ti) / Δt.

Because Δt increases, the random value is selected to

avoid falling into a local minimum. The camera can

capture a part of the 3D liver through the circular

hole.

First, we overlap a real liver by its virtual one in

the 3D space by watching the pixel states generated

by the real and virtual depth differences (Noborio

2015b). In our matching system (Figure 7), the areas

projected from the real and virtual livers into the XY

plane along the Z-axis are shown by sets of red and

blue pixels, respectively. The pixel overlapped by real

and virtual livers in the XY plane is shown in yellow.

Furthermore, the pixel overlapped by the real and

virtual livers in the XYZ space is shown in blue.

Therefore, an operator first moves the virtual liver in

the horizontal XY space by eliminating the red and

blue pixels in order to generate all yellow pixels.

Then, we move the virtual liver in the vertical XYZ

space by eliminating the yellow pixels and

simultaneously generating blue pixels.

Figure 8: We compared two kinds of motion transcription

algorithms in a real surgical room with (a) one shadow-less

lamp (b) two shadow-less lamps covered by two kinds of

invisible light filters. In our navigation, a 3D liver is always

obstructed by a cardboard box with a circular hole.

3 COMPARATIVE

EXPERIMENTAL RESULTS

In this chapter, we experimentally compared the

steepest descendent and the simulated annealing

algorithms with depth-depth matching.

Comparative Study of Depth-Image Matching with Steepest Descendent and Simulated Annealing Algorithms

Figure 9: The same rotational movement is applied for the

randomized steepest descendent (a) and simulated

annealing algorithms (b). Unfortunately, right and left are

opposite in all 2D RGB and depth images.

3.1 Experiments in a Real Surgical

Room

In this section, we present several realistic

experiments, which were conducted not in the

laboratory, but in a surgical operating room. The

experimental equipment is precisely described in

Figure 8. An acrylic plate of length 25 cm, width of

25 cm, and thickness of 2 cm was placed on the

operating table and a real liver was placed on the top

of the plate. Consequently, an operator could flexibly

move the liver. Movement of the liver was achieved

by moving the acrylic plate instead of moving the

actual liver itself.

Figure 10: The same translational movement is applied for

the randomized steepest descendent (a) and simulated

annealing algorithms (b). Unfortunately, right and left are

opposite in all 2D RGB and depth images.

Moreover, in order to conduct experiments

involving occlusion, a cardboard sheet containing a

hole of 10 cm in diameter was placed on the liver. The

surface of this corrugated board was painted in light

orange using a color spray to make it look like human

skin. The camera (Kinect v2) was attached to a

vertically movable robot. Therefore, it was able to

change its distance from the liver according to

different situations. The camera was placed

horizontally with respect to the operating table at a

height of 84 cm from the bottom of the actual liver.

The camera system was fixed by attaching metal

fittings to a metal rod. The metal rod was fixed to the

camera, which was attached to the robot. The distance

from the robot to the camera was set as 32 cm.

BIODEVICES 2018 - 11th International Conference on Biomedical Electronics and Devices

Figure 11: The light transmittance (a) and characteristics (b)

of infrared shielding filter SL999, and the light

transmittance (c) and characteristics (d) of infrared

shielding filter TS6080.

The initial positions of the real liver and the

virtual liver model were matched in the first

experimental procedure. Next, the real liver placed on

an acrylic board was covered with corrugated

cardboard. It was subjected to rotational and

translational movement within the corrugated

cardboard box. It was done to ensure that the range of

the liver visible from the hole of the cardboard did not

become less than half after the movement of the

model. In our usual experiments, we select the offset

value of 10 mm for real and virtual depth images

against the 3D real liver and its polyhedron with the

STL format in our surgical navigator. The model was

rotated 45° around the center of the z-axis during the

rotational movement (Figure 9), and it was moved by

5 cm in the y-axis direction during the parallel

movement (Figure 10). Each co-ordinate axis is

selected as shown in Figure 8.

Figure 12: (a) Virtual and real RGB images, difference

between the real and virtual depth images, and the graph of

the overlapping ratio in the randomized steepest descendent

algorithm, and (b) real RGB image and real and virtual

depth images and their difference in the simulated

annealing algorithm.

3.2 Comparison of Rotational

Following Quality of the Two

Algorithms

In this section, we compare the depth-depth

matching-based organ-following algorithms for

several surgical rotation operations. We use the

steepest descendent (randomized) and simulated

annealing algorithms as the organ-following scheme.

Each algorithm always overlaps a virtual liver with its

real liver. The quality of overlap is evaluated by the

overlapping ratio explained in the previous section. It

is individually checked for two lamps without any

infrared shielding filter, with the SL999 or with the

TS6080S (Figure 11).

The purpose behind using SL999 or TS6080S is

that the depth camera itself uses infrared illumination.

Comparative Study of Depth-Image Matching with Steepest Descendent and Simulated Annealing Algorithms

Figure 13: (a)(b) Comparative results of rotational liver operation between the randomized steepest descendent and simulated

annealing algorithms under two shadow-less lamps without any infrared shielding filter. (c)(d) Comparative results of

rotational liver operation between the randomized steepest descendent and simulated annealing algorithms under two shadow-

less lamps with the infrared shielding filter SL999. (e)(f) Comparative results of rotational liver operation between the

randomized steepest descendent and simulated annealing algorithms under two shadow-less lamps with the infrared shielding

filter TS6080S.

Kinect v2 gets the depth images by the Time of

Flight (TOF) method of projecting and receiving all

infrared rays. Therefore, the camera strictly tries to

gather the infrared rays of wavelength between 700

nm and 1000 nm. However, our shadow-less lamp

projects the infrared rays of wavelength under 400 nm

and over 1000 nm. Using our infrared filter SL999 or

TS6080S, the ultra-violet light whose wavelength is

between 10 nm and 400 nm is completely eliminated,

but the visible light whose wavelength is between 400

nm and 700 nm is not eliminated. In addition to this,

the infrared light and the radio waves over 1000 nm

are partially passed.

In our navigation system, we prepared a different

set of windows for the two algorithms, as described

in Figure 12. The reason is that the steepest

descendent (randomized) algorithm was formulated

during 2013–2015. In contrast, the simulated

annealing algorithm was independently developed

during 2016–2017.

However, in our navigation system, experimental

data such as sequences of real RGB images and depth

images during several kinds of surgical operations in

a real surgical room were completely memorized in

the PC under no infrared shielding filter. The reason

is as follows: a surgical room is always used by many

doctors, students, and researchers for surgeries,

lectures, and researches. Therefore, our experimental

data such as the sequences of lighting conditions

during surgeries, which were obtained from the surgi-

BIODEVICES 2018 - 11th International Conference on Biomedical Electronics and Devices

Figure 14: (a)(b) Comparative results of translational liver operation between the randomized steepest descendent and

simulated annealing algorithms under two shadow-less lamps without any infrared shielding filter. (c)(d) Comparative results

of translational liver operation between the randomized steepest descendent and simulated annealing algorithms under two

shadow-less lamps with the infrared shielding filter SL999. (e)(f) Comparative results of translational liver operation between

the randomized steepest descendent and simulated annealing algorithms under two shadow-less lamps with the infrared

shielding filter TS6080S.

cal room, are quite valuable. For this reason, all the

experimental information pertaining to the surgical

room was completely memorized and the algorithm

performance by varying several kinds of parameters

was checked again against the experimental

information in our laboratory. Therefore, we

compared two or more types of algorithms for the

same sequences of lighting.

A real liver is moved rotationally, and then its

virtual liver model follows the real liver. The same

rotational movement is used for the randomized

steepest descendent and simulated annealing

algorithms (Figure 9). As shown in Figure 13, the

initial overlapping ratio is over 97% (nearly equals

100%). When moved rotationally, as illustrated in

Figure 9, a variation in the overlapping ratio is

observed during the operation shown in Figure 13. In

almost all cases, the overlapping ratio obtained in the

simulated annealing algorithm was always better than

that achieved in the randomized steepest descendent

algorithm. Moreover, the overlapping ratio generated

by two lamps with TS6080S was always better than

with the other filter. As a result, the simulated

annealing algorithm using the filter TS6080S is

experimentally found to be the best with regard to the

rotational operation in liver surgery.

3.3 Comparison of Translational

Following Quality of the Two

Algorithms

A real liver is moved translationally, and then its vir-

Comparative Study of Depth-Image Matching with Steepest Descendent and Simulated Annealing Algorithms

tual liver model follows the real liver. The same

translational movement is applied to the randomized

steepest descendent and simulated annealing

algorithms (Figure 10).

As shown in Figure 14, each overlapping ratio is

over 97% (nearly equals 100%). The variation in the

overlapping ratio under translational movement

(Figure 10) is shown in Figure 14. In almost all cases,

the poorest overlapping ratio obtained in the

simulated annealing algorithm is clearly better than

that obtained in the randomized steepest descendent

algorithm. Contrary to this, the overlapping ratios

generated by two lamps without any filter are almost

the same in the simulated annealing algorithm. As a

result, with respect to the translational operation of

liver surgery, the simulated annealing algorithm is

better but using the filters is experimentally

meaningless.

4 CONCLUSIONS

In this paper, we have given several comparative

results of depth-depth-image matching-based organ-

following algorithms. Compared with our previous

laboratory experiments, or without the addition of a

shadow-less lamp, this experiment can be applied to

real-life situations such as practical surgery as

follows: the organ is artificially occluded by another

object, and the surgical operation is performed on a

real surgical bed beside two shadow-less lamps. In

this research, in addition to the comparison of two

kinds of algorithms, we checked the usefulness of two

infrared shielding filters, SL999 and TS6080S. Based

on the results, we could determine that the simulated

annealing algorithm using the filter TS6080S is the

best.

At present, we are looking forward to using an

infrared filter, which can pass light of wavelength

between 700 nm and 1000 nm. In the near future, we

will try to verify the rotational or translational

following stability of our algorithm by using more

effective infrared shielding filters.

ACKNOWLEDGEMENTS

This study was partly supported by the 2014 Grants-

in-Aid for Scientific Research (No. 26289069) from

the Ministry of Education, Culture, Sports, Science

and Technology, Japan. The study was also supported

by the 2014 Cooperation Research Fund from the

Graduate School at Osaka Electro-Communication

University.

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Comparative Study of Depth-Image Matching with Steepest Descendent and Simulated Annealing Algorithms