Shader-based Automatic Camera Layout Optimization for Mobile

Robots using Genetic Algorithm

Shuiying Wang and Ra

ul Rojas

Institute of Applied Computer Science, Freie Universit

at Berlin, Arnimallee 7,D-14195, Berlin, Germany

Keywords:

Shader, Camera Layout Optimization, Mobile Robot, Genetic Algorithm.

Abstract:

Given a mobile robot and a certain number of cameras, this paper addresses the problem of ﬁnding locations

and orientations of the cameras relative to the robot such that an optimality criteria is maximized. The optimal-

ity criteria designed in this paper emphasizes the trade-off between the coverage of area of interest around the

robot by the cameras subject to occlusion constraints and the proximity of cameras to the robot structure. Real

coded genetic algorithm is employed to search for such optimal layout and the optimality criteria serves as the

ﬁtness function. The computation intensive parts, namely the coverage and proximity analysis, are adapted

to such a form that GPU with programmable shader can be accommodated to accelerate them. A graphical

user interface tool is constructed to allow observation and checks during the optimization process. Promising

results are displayed in an experiment concerning a truck with seven cameras. The optimization framework

outlined in this paper can also be extended to optimize layout of scanning sensors like LiDAR and Radar

mounted on arbitrary structures.

1 INTRODUCTION

Mobile robots often use cameras to perceive their sur-

roundings, as is shown in the case of autonomous

vehicles with a vision system consisting of cameras,

LiDARs and Radars. As camera sensors become

more affordable and effective, an increasing number

of daily driven cars and utility vehicles are adopting

camera systems to improve driving safety. For in-

stance, a garbage truck operator needs a vision sys-

tem to secure loading and unloading of the garbage at

the rear of the truck. Another example comes from

the ﬁeld of mining truck. Huge mining trucks up to

date can be 10 meters tall and 20 meters long; as a

result, it is necessary for them to have a monitoring

system in order to avoid accidents with other small

vehicles. These mobile vehicles with such vision as-

sistants are also categorized as mobile robots in terms

of the problem domain concerned in this paper.

Efﬁciency and effectiveness are crucial in such

camera systems: the limited power supply and

space resources on mobile robots restrict the camera

amount, while desirable effects of image processing

algorithms demand extensive and detailed perception.

Therefore, an optimal layout of cameras is signiﬁ-

cantly important. However there has been little re-

search effort towards this problem in ﬁeld of mobile

robots so far. The work presented in this paper is thus

motivated to ﬁll this gap, i.e. to address the problem

of camera layout optimization for mobile robots.

Without loss of generality, given a mobile robot R,

certain area of interest A around R, a ﬁxed number N

of cameras C and a bounded continuous design space

P from which the locations and orientations of cam-

eras are chosen; we are focusing on ﬁnding a set of

camera parameters P

optimal

that can maximize an ob-

jective function F

implying the trade-off between the

coverage of the camera system over A and the prox-

imity of cameras to the robot structure. Equation (1)

gives a mathematical expression of the problem. In

terms of evaluation of a certain layout, coverage cal-

culation and the computation of proximity of cameras

to the robot structure are two key issues among oth-

ers. We adapt the coverage analysis and proximity

computation to such a form that GPU with shader can

be adopted to enhance the computation. Genetic al-

gorithm (GA) is employed as optimization method.

Our solution framework can also be applied to hy-

brid sensor system consisting of cameras, LiDARs

and Radars.

optimal

= argmax

∈P

, R, A) (1)

With problem deﬁnition stated above, main con-

tributions of our work are as follows:

153

Wang S. and Rojas R..

Shader-based Automatic Camera Layout Optimization for Mobile Robots using Genetic Algorithm.

DOI: 10.5220/0004692201530160

In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications (GRAPP-2014), pages 153-160

ISBN: 978-989-758-002-4

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

(1) First attempt to take into account in camera

layout optimization the proximity of the cameras to

the structure on which they are mounted and to trans-

form the problem in a way that shader can be em-

ployed to enhance the optimization process.

(2) Detailed presentation of a GUI Tool frame-

work allowing observations and checks in optimiza-

tion process.

(3) First attempt to adopt real coded GA to search

for the optimal layout of a camera system in the

context of mobile robot over a continuous design

space, as opposed to using preselected camera can-

didates with discrete location and orientation values

presented in works in other contexts such as security

monitoring system.

The remaining of this paper is organized as fol-

lows: in Section 2 a review of related work is il-

lustrated and our approach is justiﬁed in comparison

with them. In Section 3 the methodology with respect

to coverage and proximity analysis is presented. In

Section 4 the instantiation of the methodology using

shader are described in detail. After that, GA op-

timization overview and implementation details are

presented in Section 5. Section 6 depicts the GUI

Tool. The experiment and related results about cam-

era layout optimization for a truck are presented in

Section 7. Section 8 contains a conclusion of this

work and directions of future work.

2 RELATED WORK

Research in the area of camera layout optimization

has roots in the Art Gallery Problem (AGP), an ex-

tensively studied topic in the ﬁeld of computational

geometry. The purpose of AGP is to ﬁnd the posi-

tions of a minimum number of guards such that every

point in a polygon is within sight of at least one guard.

Extensive reviews about AGP and its variants can

be found in (O’Rourke, 1987),(Erdem and Sclaroff,

2006),(Murray et al., 2007). In short, the determi-

nation of exact solution for AGP is NP-hard, while

many efﬁcient algorithms and heuristics are available

to ensure a suboptimal decision; theoretical results

concerning AGP are based on unrealistic assumptions

such as inﬁnite Field Of View (FOV) for cameras and

therefore they cannot provide effective approaches to

real world problems.

Consequently, a large majority of research related

to optimization of camera conﬁguration with more re-

alistic assumptions has emerged and most of it is set in

the context of in- or outdoor surveillance and monitor-

ing system, where video camera systems are widely

employed and an optimal arrangement of cameras is

crucial.

In (David et al., 2007) a sensor placement ap-

proach was proposed for monitoring human activities

in indoor scenes. Their goal is to determine a sub-

set of preselected sensor samples such that the sensor

cost is minimized and the required scene is covered.

Firstly, the polygons in the scene are sampled into a

list of points and the points covered by each sensor

candidate are determined via a ray tracing algorithm

from Matlab. Then branch and bound algorithm and

GA are implemented respectively for an optimal solu-

tion. The approach is exempliﬁed with cameras while

the authors stated that it also applies to other camera-

like sensors.

With the same basic idea as (David et al., 2007),

(Erdem and Sclaroff, 2006) proposed a radial sweep

visibility algorithm to handle holes in the ﬂoor dur-

ing ray tracing rendering in order to consider the oc-

clusions caused by them. In terms of optimization

method, it was asserted that the optimality of the ﬁnal

result would depend on the density of the preselected

camera samples with discrete location and orientation

values.

Although it was stated in (David et al., 2007) and

(Erdem and Sclaroff, 2006) within their methodology

that the problems are set in a 3D context, yet the im-

plementations were carried out in simpliﬁed 2D ver-

sions.

A framework was developed in (Murray et al.,

2007) to optimize video sensor placement for secu-

rity monitoring in an urban area. They employed Ge-

ographical Information System (GIS) to implement

visibility analysis(i.e. coverage analysis) and adopted

a commercial optimization software to search for the

optimal solution. They focused on illustrating the ef-

fects of various trade-offs among different areas of in-

terest via implementing the optimization framework.

Research in (Becker et al., 2009) focused on cam-

era layout optimization for detection of human be-

ings. Instead of a planar area of interest, a 3D volume

of interest extruded from horizontal surfaces up to the

height of a human being is taken as the target space.

The 3D volume is sampled into a series of points and

the coverage is computed by a ray tracing algorithm.

A greedy heuristic is followed in the selection of cam-

eras.

An automatic approach is proposed in (Fleishman

et al., 2000) for choosing camera positions that can

guarantee an image-based modeling of high quality.

In addition to the coverage requirements, the rendered

images should be qualiﬁed for the 3D scene mod-

elling task. Correspondingly, the coverage quality is

stressed. They mentioned that they employ 3D hard-

ware to speed up the visibility analysis; thus our vis-

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154

ibility analysis method might be similar to theirs in

scope.

A wireless sensor network optimization using

multi-objective GA(MOGA) is described in (Jourdan

and de Weck, 2004). Besides horizontal and verti-

cal coordinates of the sensors, they also introduce the

sensor number into the design vector. The MOGA

provides the end-user with a set of Pareto-optimal lay-

outs illustrating the trade-off between different objec-

tives, one of which is the number of deployed sensors.

To conclude, the methodology and implementa-

tion presented in our work suits very well to the con-

text of mobile robots. Firstly, in contrast to the huge

amount of sensors and quite large area of interest in

contexts of surveillance system mentioned above, the

number of sensors mounted on a robot is very lim-

ited and thus the area of interest of such a camera

system is relatively small. Consequently, a more ac-

curate coverage analysis considering occlusion con-

straints imposed by the robot body itself is necessary

and tractable in terms of time consumption. Secondly,

mobile robots are always in dynamic states due to

motion and suffer from frequent contact with its sur-

roundings, thus it is better to place the sensors close

to the robot body for the sake of compactness. As

a result, the proximity between the cameras and the

robot body should be considered in the evaluation of a

camera layout. Lastly, as the design space of the opti-

mization problem in the case of mobile robot is much

smaller than that of in-or outdoor surveillance sys-

tems, we do not need to preselect sensor candidates;

instead, we use GA to search over a continuous de-

sign space with bounding limits deﬁned by the robot

body structure and the target area, which is otherwise

computationally prohibitive in terms of surveillance

systems involving large areas.

3 METHODOLOGY

The evaluation of a given layout according to the op-

timality criteria that emphasize the trade-off between

coverage and proximity is the most computation in-

tensive part in the problem focused in this paper. We

formulate the coverage and proximity analysis in such

a way that rasterization based rendering technique

can be employed to enhance the computation via the

use of GPU. The programmable shader in the render-

ing pipeline is designed to record the information we

need.

3.1 Coverage Analysis

As the FOV of a camera can be represented as a frus-

tum, the coverage analysis within the scope of this

paper can be formulated in the following way: given

several frustums , a set of primitives like points, lines

and polygons serving as area of interest to be covered

and another set of such primitives imposing occlu-

sions, the problem is to calculate the intersection area

of the frustums and the area of interest subject to the

occlusions. It is almost intractable in terms of com-

putational intensity to obtain accurate results for such

problems when the primitives and the frustums are in

a large amount and positioned irregularly, which is

just the case as presented in this paper. As a result,

the coverage analysis algorithm designed in this pa-

per implies a trade-off between the accuracy and the

time consumption and is based on the parallel com-

putation architecture of GPU and the ﬂexibility of the

programmable shader. The corresponding method is

presented in the following:

(1) The set of primitives composing the area of in-

terest is discretized into small entities, with each as-

signed a speciﬁc identity number. All the primitives

producing occlusions are assigned one common iden-

tity number.

(2) While normally the rendering result of the

frustum by GPU is an image of pixels with each con-

taining color information of the targeted entity(i.e, the

entity that lies within FOV of the frustum and is used

to provide information for that speciﬁc pixel during

image rasterization), a speciﬁc shader can be designed

to record the identity number of the entity rather than

the color information in the pixel.

(3) After all the frustums are rendered, the cover-

age is calculated according to the set of entities be-

longing to the area of interest recorded in the images.

The fact that an entity would appear more than once

means that some part of the covered areas of differ-

ent frustums are overlapped, so in such case only one

instance of the entity should be considered. Weights

can be assigned to the entities to indicate their various

degrees of importance.

3.2 Proximity Analysis

Proximity analysis can be reduced to ﬁnding the

shortest euclidean distance between a point and a set

of primitives in 3D space (i.e., the robot in our case).

Such problem is faced with the same challenge as the

coverage analysis. The common method to deal with

it is to make use of a bounding box comprising the set

of primitives and calculate the shortest distance of the

point to the bounding box. As the body structure of a

mobile robot is complicated and irregular, the bound-

ing box solution would result in a large discrepancy

between the real distance and the approximated one.

Shader-basedAutomaticCameraLayoutOptimizationforMobileRobotsusingGeneticAlgorithm

155

The method proposed in this paper can yield a more

accurate proximity calculation with the extra compu-

tation cost incurred being discounted to some extent

by leveraging the parallel computation architecture of

GPU. The resulted method is in principle similar to

that of coverage analysis. The following is applied to

each camera separately:

(1) A certain amount of frustums with origins at

the position of one camera are constructed and ori-

ented in such a way that they can together cover the

3D space around that camera.

(2) The shader for each frustum rendering is de-

signed to record in each pixel the identity number of

the targeted entity as well as its distance to the origin

of the frustum (i.e.,the location of the camera).

(3) The shortest distance (i.e., the proximity) can

be obtained by comparing the distance values saved

in all the pixels with the identity number of the robot

in the images rendered by all the frustums.

Finally, the largest proximity among the member

cameras is assigned to be the proximity of the camera

system. Figure 1 demonstrates the effect of proximity

analysis instantiated with 6 frustums for one camera.

(a) (b) (c) (d)

Figure 1: One camera location with 6 frustums: ψ = 0

◦

, θ =

◦

, 90

◦

, 180

◦

, 270

◦

respectively; θ = 0

◦

, ψ = 90

◦

and 270

◦

respectively. φ = 0

◦

for all. (a): 1 frustum; (b): the other 5

frustums; (c): 6 frustums with high resolution images; (d):

6 frustums with low resolution images.

4 INSTANTIATION

In this section, the implementation details with re-

gard to the methodology presented in Section 3 are

described. As the coverage and proximity analysis

are similar in principle with main differences lying in

the information recorded in shader, we only empha-

size the coverage analysis here. The instantiation is

set in the scenario of camera system layout optimiza-

tion for a truck. As is pointed out earlier, a truck with

a camera system is also regarded as a mobile robot

within the scope of this paper.

4.1 Mobile Robot Modelling

The mobile robot model is a 3D mesh composed of

geometric primitives like points, lines and polygons.

It has two roles in the scenario: cameras accommo-

dation and camera view occlusion. In terms of ge-

netic algorithm implementation, we specify a bound-

ing box on the robot as the location design space for

the cameras. With regard to coverage and proxim-

ity analysis, we assign an identity number IDR to the

robot as a common property for all its vertices such

that it can be differentiated from the area of interest.

4.2 Area of Interest Modelling

As surroundings of the mobile robot always change,

it is hard to deﬁne a universal target space. As a re-

sult, we specify a planar area around the robot as the

area of interest. While this is a a naive assumption,

it can be adapted to more complex versions as long

as more detailed information about the environment

is available.

The planar area is discretized into a grid to fa-

cilitate coverage calculation and thus the calculation

accuracy depends in part on the resolution of the

grid. Two arrays, WeightArray(WA) of ﬂoat type

and OccupancyArray(OA) of binary type with each

of size ArraySize(AS), are allocated in shared mem-

ory to store weights and states of coverage of the grid

cells respectively. Each grid cell is assigned a speciﬁc

identity number IndexID identical to its index in the

arrays to communicate if any cell is covered by any

camera FOV. It should be noted that the robot identity

number IDR must be outside the scope of the array

index and that the weights are determined according

to speciﬁc requirements from the area of interest. The

element in OA is set to the value of 1 if the grid cell

related to it is covered; thus the coverage can be rep-

resented in the form of (2). R and A are implicitly

included in (2) because they have inﬂuences on the

values of WA(i) and OA(i).

(P, R, A) =

AS−1

∑

i=0

(WA(i) × OA(i))

AS−1

∑

i=0

(WA(i))

(2)

In combination with the proximity, the objective

function F

in (1) can be formulated as (3), where the

value of α implies the trade-off between coverage and

proximity. The range of the ﬁtness function is [0, 1].

(P, R, A) = C

αProximity

(3)

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156

4.3 Camera Modelling

The camera, namely the frustum, is modelled by

the camera node speciﬁed in OpenSceneGraph(OSG).

More details can be found in (Wang et al., 2012),

where the simulated Radar works in a similar way

to the frustums for coverage analysis while the main

function of simulated LiDAR corresponds to the role

of frustums for proximity analysis. Cameras have

intrinsic and extrinsic properties. The intrinsic ones

concerned in this paper include mainly depth of ﬁeld

bounded by Near and Far values, vertical FOV, hor-

izontal FOV, vertical resolution and horizontal res-

olution; the ﬁrst three deﬁne the frustum which in

turn determines the transformation matrix from cam-

era coordinates to the 2D image arrangement, while

the last two specify the image resolution. The ex-

trinsic ones contain location (x, y, z) and orientation

(yaw(ψ), pitch(θ), roll(φ)) which specify the trans-

formation matrix from world coordinates to the cam-

era coordinates. In our work only the extrinsic param-

eters are taken as design variables while the intrinsic

ones embodying the camera type remain unchanged

during the optimization.

As we evaluate the coordinated performance of

all the cameras in the camera system, we construct

a class MultiCameraModel comprising both intrin-

sic and extrinsic properties necessary in the mod-

elling of one set of N cameras. The counterpart

of MultiCameraModel with respect to GA is an-

other class MulticameraIndividual involving only

the extrinsic properties. There is only one instance

of MultiCameraModel in shared memory, whereas

the number of MulticameraIndividual instances re-

main consistent with the population size speciﬁed for

GA optimization. During the coverage analysis, a

MulticameraIndividual would substitute for extrin-

sic properties of the MultiCameraModel such that the

camera system would be remodelled and the corre-

sponding coverage would be calculated. In addition,

three variables, AllImageProcessed, TotalImages

and ProcessedImages, are allocated in shared mem-

ory to assist the coverage analysis; TotalImages is of

value N while ProcessedImages changes in value on

the ﬂy. The coverage analysis framework is elabo-

rated in subsection 4.4.

A vertex shader and a fragment shader serve in

the rendering pipeline of the camera model such that

the identity number of the objects within the camera

view can be recorded during the rendering stage and

analysed thereafter. Related shader programming is

illustrated in Figure 2. The targeted position of each

pixel is also recorded for displaying of the vision sys-

tem effect. As each of the four elements composing

one fragment ranges from 0 to 1, the identity number

and position must be divided by certain ScaleFactors

before assigned to the FragData(pixel). More details

about shader application in camera-like sensor mod-

elling are available in (Wang et al., 2012).

A class PostRenderingAnalysis is attached to the

camera model for image analysis implemented for

each camera during coverage analysis. The pseudo

code of this procedure is shown in Algorithm.1, where

the letter M indicates the index of the element that

stores IndexID of targeted entity in FragData.

Encode x,y,z, objectID in FragData with

each divided by a proper scale factor

Fragment

shader

Record pos(x,y,z) in eye space

vertex

shader

pos(x,y,z)

objectID

out

Uniform

out

Figure 2: Vertex and fragment shader programming.

Algorithm 1: Image analysis for one camera.

1: function POSTRENDERINGANALYSIS( )

2: if !AllImageProcessed then

3: for Frag ← all frags in current image do

4: Ob jectID ← Frag[M] × ScaleFactor

5: if 0 ≤ Ob jectID < ArraySize then

6: OccupancyArray[Ob jectID] ← 1

7: end if

8: end for

9: ProcessedImages ← ProcessedImages +

10: if ProcessedImages == TotalImages

then

11: AllImageProcessed ← true

12: end if

13: end if

14: end function

4.4 Coverage Analysis

Coverage analysis serves as part of ﬁtness evaluation

in GA. There are three modules involved in coverage

analysis: GA, shared memory and simulator (camera

modelling and rendering). GA and simulator commu-

nicate with each other via shared memory. Basically,

individuals of GA iteratively substitute for the extrin-

sic parameters of the MultiCameraModel, leading to

reconstructions of the camera models. After images

in the frame buffer are refreshed and analysed, GA

summarizes the ﬁtness value in terms of coverage ac-

cording to (2). Figure 3 displays a detailed implemen-

tation.

Shader-basedAutomaticCameraLayoutOptimizationforMobileRobotsusingGeneticAlgorithm

157

Input: each individual

in one generation

Assign MultiCameraIndividual

(extrinsic parameters)

to MultiCameraModel

MultiCameraChanged

true

ProcessedImages

AllImagesProcessed

true

MultiCameraChanged ?

false

true

AllImagesProcessed

false

AllImagesProcessed ?

true

false

Calculate fitness

based on Equation (2)

Output: fitness of

this individual

Shared Memory

MultiCameraModel

(extrinsic & intrinsic

parameters of

N cameras)

MultiCameraChanged

ProcessedImages

AllImagesProcessed

Camera system reconstruction

Camera1

CameraN

Area of interest

Robot

Camera2

MultiCameraChanged ?

false

true

Camera system rendering:

Vertex shder

Fragment shder

Image data

Frame buffer

PostRenderingAnalysis

GPU

CPU

OccupancyArray

Array of 0

wait

Visibility analysis in GA

OccupancyArray

Area of interest

Robot

Area of interest

Robot

Simulator

MultiCameraChanged = false

TotalImages = N

Figure 3: Coverage analysis implementation.

5 GENETIC ALGORITHM

IMPLEMENTATION

5.1 Justiﬁcation for Applying GA

The main characteristics of the optimization problem

deﬁned in this work are as follows:

• It is hard to present the objective in terms of the

design variables: expression of the intersection of

the ground with one single frustum in terms of

design parameters is already very difﬁcult, not to

mention the case where the overlapping area of

every two intersections and the occlusions of the

mobile robot are considered.

• The quantitative and qualitative relationship be-

tween each design variable and the objective is

also difﬁcult to determine. Due to the two reasons

mentioned above, classical slope based optimiza-

tion algorithm is not applicable for our task.

• The design space is continuous and multi-

dimensional. As the time complexity grows expo-

nentially with the number of design parameters,

it would be computationally intractable to simply

discretize the design space and perform a brute

force algorithm.

As a result, GA, an efﬁcient tool in handling op-

timization problems involving functions intractable

by classical optimization methods(Sharapov and Lap-

shin, 2006), is chosen for resolving our problem.

5.2 Optimization Framework

GA imitates natural selection process in search of a

better solution (Holland, 1992). Therefore its basic

idea is to iteratively reproduce a new generation of

individuals through operating on the old one; these

operations should be designed in such a way that the

new generation in general adapts to the environment

at least as well as, if not better than, the old one. Com-

mon operations are selection, crossover and mutation

(Goldberg, 1989). As operations on the individuals

are probabilistic, GA optimization is also a stochas-

tic process which cannot ensure that a solution can be

found. In (Sharapov and Lapshin, 2006) some proofs

on the convergence of several genetic algorithm vari-

ants in the mean are provided. In general, the proba-

bility of operations and the design of operations them-

selves are crucial in terms of search efﬁciency and

global optimality of the converged solution. Our GA

optimization framework is shown in Figure 4.

Start

Problem & GA

instantiation

Population

initialization

Fitness evaluation

Termination condition

satisfied?

Yes

End

Crossover

Mutation

Selection

New

population

Manual check

Manual

check

Shared

memory

GUI Tool

Simulator

Manual check

enabled?

Yes

True

Wait

for

while

False

Go to next?

(Coverage analysis)

Go to next = false

Figure 4: GA optimization ﬂow chart.

5.3 Implementation Details

The following describes the adaptations of GA for

solving the problem deﬁned in this paper.

• Individual: MultiCameraIndividual containing

design variables of N cameras, as mentioned in

Section 4, is represented in the following way:

[x1, y1, z1, ψ1, θ1, φ1, x2, y2, ......, φN] (4)

• Population: The population size is empirically set

to be around 10 times the number of design vari-

ables of the individual. The initial population is

generated by pseudo random number generator.

• Selection: Detailed discussion of selection meth-

ods are available in (Sivaraj and Ravichandran,

2011). Traditional Roulette Wheel selection is

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158

utilized in this work and thus the probability for

each individual to get involved in crossover is pro-

portionate to their ﬁtness. Elitist selection is also

applied to ensure that individual with the highest

ﬁtness is always passed to the next generation.

• Crossover and mutation: One-point and two-point

crossover are undertaken respectively, each with

two crossover strategies: crossover per camera,

crossover per design variable. The results turned

out to be almost the same, though. Mutation is

applied on one stochastically chosen parameter of

each camera of randomly selected individual cam-

era system.

• Random number generator: Pseudo random

number generator proposed in (Matsumoto and

Nishimura, 1998) is adopted in this work. We ob-

serve that random number is crucial to the success

of the optimization.

6 GUI TOOL

The GUI Tool contains a display for observation and a

GUI control panel facilitating observation and checks

of the optimization progress and result. The GUI Tool

functionalities and framework is presented in Figure 5

while a snapshot of the GUI Tool is shown in Figure

6. Via the manual check, the GA pauses while the

user can check the performance of any individual in

current generation via GUI Tool. The user can also

modify the individual and GA parameters to inﬂuence

the GA process if necessary.

GA Process

Manual

check

Coverage&Proximity

Analysis

Shared Memory

EnableCheck

GoToNext

GUI Control Panel

Enable Check

Check coverage

of an individual

Change

MultiCameraModel

Update Individual

according to

MultiCameraModel

Go to next

MultiCamera-

Model

Update modified

Individual

GUI Display

GA fitness Display

Simulator Display(Individual coverage)

Simulator

Read or Write

Memory

Function

invoke

Inter-Module

communication

Figure 5: GUI Tool functionalities and framework.

7 EXPERIMENT AND RESULTS

In the experiment we consider the problem of a truck

and its vision system of 7 cameras. The scenario is

shown in Figure 6. The experiment is carried out on a

computer with 4 core-Intel i5 CPU and GeForce GT

330 with 1024MB memory.

Figure 6: Problem instantiation and part of GUI Tool.

7.1 Problem Modelling

• Design variable constraints: The yellow bounding

box in Figure 6 suggests the design space of cam-

era locations(indicated by the blue box) while the

orientations are bounded within ψ : [0

◦

, 360

◦

], θ :

[50

◦

, 65

◦

], φ : [0

◦

, 90

◦

]. The red frustum displays

the camera modelling. The white points on the

ﬂoor and the truck represent the coverage of cam-

era view and the occlusion effect imposed by the

truck respectively. Image resolution of each cam-

era is 75× 48 for coverage analysis and 180 × 180

for proximity analysis.

• Area of interest: A grid of 2280 cells represents

an area with 5m offset surrounding a truck with

length of 8m and width of 2.5m, as is shown in

Figure 6 with each cell drawn in a random colour.

Weights of all the cells are set equally to 1.

• GA: Population size is 480; crossover rate is 0.99;

mutation rate is 0.1; elitism rate is 1%; it termi-

nates at the 120th iteration.

• Fitness function: refer to (3). We demonstrate two

cases in the following with α equal to 0 and 1 re-

spectively.

7.2 Results

The performance of the camera system after 120 it-

erations is shown in Figure 7 and Figure 8. Figure 9

displays the corresponding evolution processes of 120

iterations in terms of best (green), average (blue) and

worst (red) ﬁtness , and also of proximity (yellow) and

coverage(magenta) for the individual with the best ﬁt-

ness when α is not 0 in the ﬁtness function. It takes

Shader-basedAutomaticCameraLayoutOptimizationforMobileRobotsusingGeneticAlgorithm

159

about 80 minutes in average for optimization without

proximity analysis while those with proximity analy-

sis last about 600 minutes.

(a) α = 0 (b) α = 1

Figure 7: Coverage performance of the optimal layouts: (a)

coverage = 0.92, (b) coverage = 0.89.

(a) α = 0 (b) α = 1

Figure 8: Camera locations of the optimal layouts: (a) Prox-

imity = 0.39(m), (b) Proximity = 0.21(m).

(a) α = 0 (b) α = 1

Figure 9: Fitness evolution of 120 iterations.

8 CONCLUSIONS AND FUTURE

WORK

In this paper, we formulate the camera layout opti-

mization problem for a mobile robot and propose an

automatic approach using real coded GA. Coverage

and proximity analysis are accelerated by GPU with

shader. A GUI Tool for observation and checks in

GA process is depicted. The result demonstrated in

the experiment concerning a truck is promising. As

future work, we will focus on following aspects: (1)

modify the ﬁtness function to consider the require-

ments from the image-processing stage, e.g. distance

of neighbouring targeted points on the planar area (2)

investigate into the practical guidelines in choosing

the parameters of genetic algorithm.

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