Topological Map Building and Path Estimation Using Global-appearance

Image Descriptors

F. Amor

, L. Pay

, O. Reinoso

, W. Mayol-Cuevas

and A. Calway

Dep. de Ingenier

ıa de Sistemas y Autom

atica, Miguel Hern

andez University,

Avda. de la Universidad, s/n. 03202, Elche (Alicante), Spain

Department of Computer Science, University of Bristol,

Woodland Road BS8 1UB, Bristol, United Kingdom

Keywords:

Map Building, Topological Graph, Image Scale Comparison, Global-appearance Descriptor.

Abstract:

Visual-based navigation has been a source of numerous researches in the ﬁeld of mobile robotics. In this paper

we present a topological map building and localization algorithm using wide-angle scenes. Global-appearance

descriptors are used in order to optimally represent the visual information. First, we build a topological graph

that represents the navigation environment. Each node of the graph is a different position within the area, and it

is composed of a collection of images that covers the complete ﬁeld of view. We use the information provided

by a camera that is mounted on the mobile robot when it travels along some routes between the nodes in the

graph. With this aim, we estimate the relative position of each node using the visual information stored. Once

the map is built, we propose a localization system that is able to estimate the location of the mobile not only

in the nodes but also on intermediate positions using the visual information. The approach has been evaluated

and shows good performance in real indoor scenarios under realistic illumination conditions.

1 INTRODUCTION

The autonomous navigation of a mobile agent in a

certain environment usually requires an inner repre-

sentation of the area, i.e. a map, that the robot will

interpret in order to estimate its current position using

the information provided by the sensors it is equipped

with. Among all the possible sensors a robot can

use to achieve that purpose, in this paper we focus

on a visual system, since it constitutes a rich source

of information and the sensors are relatively inexpen-

sive. Speciﬁcally, in this work we use a ﬁsh-eye sin-

gle camera, which provides wide angle images of the

environment.

A key task in vision based navigation is match-

ing. Through the matching of the current robot sensor

view with previous information that constitutes the

robot’s map, it is possible to carry out its localization.

Usually, this is achieved by extracting some features

from the image in order to create a useful descriptor

of the scene with a relative low dimension to make it

useful in real time operation. In this task, two main

categories can be found: feature based and global-

appearance based descriptors. The ﬁrst approach is

based on the extraction of signiﬁcant points or regions

from the scene. Popular examples include SIFT fea-

tures (Lowe, 2004) or SURF (Murillo et al., 2007).

On the other hand, global-appearance descriptors try

to describe the scene as a whole, without the extrac-

tion of local features or regions. For example, (Krose

et al., 2007) make use of PCA (Principal Component

Analysis) to image processing, and (Menegatti et al.,

2004) take proﬁt of the properties of the Discrete

Fourier Transform (DFT) of panoramic images in or-

der to build a descriptor that is invariant to the robot’s

orientation. Regarding the map representation of the

environment, the existing research can be categorized

in two main approaches: metric and topological. Met-

ric maps include information such as distances respect

to a predeﬁned coordinate system. In this sense, we

can ﬁnd examples as (Moravec and Elfes, 1985), that

presents a system based on a sonar sensor applied

to robot navigation, and (Gil et al., 2010), that de-

scribes an approach to solve the SLAM problem us-

ing a team of robots with a map represented by the

three-dimensional position of visual landmarks. In

contrast, topological techniques represent the envi-

ronment through a graph-based representation. The

nodes correspond to a feature or zone of the environ-

ment, whereas the edges represent the connectivity

385

Amoros F., Paya L., Reinoso O., Mayol-Cuevas W. and Calway A..

Topological Map Building and Path Estimation Using Global-appearance Image Descriptors.

DOI: 10.5220/0004485203850392

In Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2013), pages 385-392

ISBN: 978-989-8565-71-6

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

between the nodes. In (Gaspar et al., 2000) a visual-

based navigation system is presented using an omni-

directional camera and a topological map as a rep-

resentation in structured indoor ofﬁce environments.

(Frizera et al., 1998) describe a similar system which

is developed using a single camera.

In (Cummins and Newman, 2009), a SLAM sys-

tem called FAB-MAP is presented. The description of

the scenes is based on landmark extraction. Speciﬁ-

cally, they use SURF features, and their experimental

dataset is a very large scale collection of outdoor om-

nidirectional images. Our aim is to develop a similar

system but using a wide-angle camera (which is more

economical than catadioptric or spherical vision cam-

era systems). Another difference is the kind of infor-

mation we use to describe the images, since we use

global-appearance descriptors.

The ﬁrst step in our work consists in building a

map of the environment. We use a graph representa-

tion. In this representation, each node is composed of

8 wide-angle images that cover the complete ﬁeld of

view from a position in the environment to map, and

the edges represent the connectivity between nodes to

estim.

In order to estimate the topological relationships

between nodes, we use the information extracted from

a set of images captured along some routes which pass

through the previously captured nodes. As a contribu-

tion of this work, we apply a multi-scale analysis of

the route and node’s images in order to increase the

similarity between them when we move away form

a node. From this analysis, we obtain both an in-

crease of correct matching of route images in the map

database, and also a measurement of the relative po-

sition of the compared scenes.

Once the map is built, as a second step we have

designed a path estimation algorithm that also takes

proﬁt of that scale analysis to extrapolate the position

of the route scenes not only in the nodes but also in

intermediate points. The algorithm, which is also a

contribution of this work, introduces a weight func-

tion in order to improve the localization precision.

The remainder of the paper is structured as fol-

lows. Section 2 introduces the features of the

dataset used in the experimental part, and the global-

appearance descriptor selected in order to represent

the scenes. Section 3 presents the algorithm devel-

oped to build the topological map. In Section 4 we

explain the system that builds the representation of

route paths, and experimental results. Finally, in Sec-

tion 5 we summarize the main ideas obtained in this

work.

TERMINOLOGY: We use the term node to refer

to a collection of eight images captured from the same

position on the ground plane every 45

◦

, covering the

complete ﬁeld of view around that position. We de-

note the collection of images of the nodes as map’s

images or database’s images. The graph that rep-

resents the topological layout of the nodes is named

map. The process of ﬁnding the topological connec-

tion between nodes and their relative position is the

map building. We call the relative position between

nodes topological distance. When we write image

distance we refer to the Euclidean distance between

the descriptors of two images. The topological dis-

tance between two images is denoted as l, and the

topological distance between nodes as c.

2 DATA SET AND DESCRIPTOR

FEATURES

In this section, we present the features of the images’

data set, and the global-appearance technique we use

in order to create a descriptor of the scenes.

The images are captured using a ﬁsheye lens cam-

era. We choose this kind of lens due to its wide-angle

view. Speciﬁcally, the model used is the Hero2 of Go-

Pro (Woodman Labs, 2013). The angle of view of the

images is 127

◦

. Due to the ﬁsheye lens, the scenes

present a distortion that makes it impossible to ob-

tain useful information from the images using global-

appearance descriptors, since they are based on the

spatial distribution and disposition of the elements in

the scene, and the distortion makes the elements to ap-

pear altered. For that reason, we use the Matlab Tool-

box OCamCalib in order to calibrating the camera

and computing the undistorted scenes from the origi-

nal images (Scaramuzza et al., 2006). In the reminder

of the paper, the term image refers to the undistorted

transform of the original scenes.

Since the aim of this work is to solve the problem

of place recognition using the global-appearance of

images, it is necessary to use descriptors that concen-

trate the visual information of the image as a whole,

being also interesting the robustness against illumi-

nation changes and the capacity of dealing with little

changes in the orientation of the scenes. Some works,

as (Paya et al., 2009), have compared the perfor-

mance of some global-appearance descriptors. Taking

them into account, we have decided to choose Gist-

Gabor descriptor (Torralba, 2003), (Oliva and Tor-

ralba, 2001) as it presents a good performance in im-

age retrieval when working with real indoor images.

It also shows a reasonable computational cost. With

an image’s size of 64x32 pixels, the algorithm spent

0.0442 seconds to compute the descriptor using Mat-

lab R2009b running over a 2.8 GHz Quad-Core Intel

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Table 1: Number of Images per Area

# Images Area 1 # Images Area 2

Nodes 352 52

Route 1 110 100

Route 2 50 72

Route 3 67 66

Route 4 58 125

Route 5 62 -

Route 6 46 -

Route 7 69 -

Route 8 67 -

Route 9 40 -

Xeon processor, requiring 4,096 bytes of memory per

image.

The dataset is divided in two different areas. The

Area 1 is composed of 44 nodes, whereas Area 2 has

13 nodes. The nodes are taken every 2 meters as a

rule, but in places where an important change of ap-

pearance in the area is produced, i.e. crossing a door,

we capture a new node independently of the distance.

For that reason, the distance may be lower. As stated

above, each node has 8 images captured every 45

◦

approximately regarding the ﬂoor plane, covering the

complete ﬁeld of view.

We have also captured images along routes in both

areas. The information of those routes is used ﬁrst

in order to ﬁnd the topological relationships between

nodes and build the graph representation in the map

building task, and next to carry out the path estima-

tion of those routes in the localization experiments.

Regarding the routes, the images are taken every 0.5

meters in Area 1, and every 0.2 meters in Area 2. In

changes of direction, we increase the frequency of im-

ages captured. We take a minimum of four images per

position when a change of orientation is produced. In

Area 2, that frequency increases with a minimum of

6 images per position. In Fig. 1 we can see the dis-

tribution of the nodes and the routes in a synthetic

representation.

3 MAP BUILDING

In this section we describe the algorithm we have de-

veloped in order to create the robot’s inner represen-

tation of the environment. Since we propose a topo-

logical representation, the map building process relies

on ﬁnding the adjacency relations and relative dispo-

sition of the nodes to create the map. For that pur-

pose, we use the route images. So then, the map is

built as a graph were the nodes represent a location

of the environment, whereas the edges provides infor-

(a)

(b)

Figure 1: Synthetic distribution of nodes and routes for (a)

Area 1 and (b) Area 2.

mation about the topological distance and direction of

adjacent nodes. We have no previous information nei-

ther about the order of the nodes nor its disposition in

the world. However, we know in which order the 8

images of each node were captured. The node’s im-

ages make up a retrieval database. The system uses

the images of the route to arrange and ﬁnd the spatial

relations between nodes by matching its images with

the map’s images. Since the route images are ordered,

we add information to the map’s graph incrementally

through the retrieval of the node’s images using the

route scenes.

In this process, we make use of some artiﬁcial

zooms of the images to increment the likelihood of

retrieving the correct nearest node’s image given a

route image. In Fig. 2 we can see a representation

of the disposition of the route’s images regarding the

nodes, and examples of the scenes. Figure 2(b) is an

image of the route, Fig. 2(a) is the closest node’s

image, and Fig. 2(a’) represents a zoom in of the

node’s image. Comparing the route image with both

the original node’s image and its zooms in, we can

realize that the appearance is more similar with the

zoomed scene. This is especially interesting for ﬁnd-

TopologicalMapBuildingandPathEstimationUsingGlobal-appearanceImageDescriptors

387

ing the correspondence of images located halfway of

two nodes, since the similarity in that positions signif-

icantly decreases regarding the nearest nodes. Using

the zooms we increase the probability of a correct re-

trieval.

In our algorithm, we use zooms in of both the

node’s images and the route’s images. Given a

route image, the algorithm compares several scales of

this image with different scale representations of the

node’s images. After these comparisons, we select

the experiment with the minimum image distance. s

and s

represent the speciﬁc scale values of the node

and the route images respectively for which the min-

imum image distance happens during the retrieval.

The topological distance l between the route image

and the node can be estimated using that coefﬁcients

as:

l = s

− s

(1)

As we can see in Fig. 2, if an image of the route (b)

is ahead a node (a), the most similar appearance will

correspond to a zoom in the node’s image (a’). That

would mean a positive value of l. On the other hand,

if the current position of the route is behind a node,

the most similar appearance is between a zoom in of

the image test (c’) and the node’s image (d), which

means a negative value of l.

First, we have to build the map database Z. This

database will be used in order to carry out the re-

trieval node’s scenes using the route images. For

that purpose, we compute the descriptor z

∈ R

1×y

of the node imagery, being y the number of compo-

nents of each descriptor. The descriptors are stored as

the columns of a matrix, which is the map database

Z = [z

. . . z

], being m the number of im-

ages of the database, that corresponds with the num-

ber of nodes multiplied by the number of orientations

per node and by the number of zooms per node’s im-

age.

Since the descriptors are stored following the

same order as the database images, it is possible to

ﬁnd out the corresponding node n, orientation in the

node θ and image scale s

of an image from the po-

sition of its descriptor in the matrix Z. Denoting i as

the number of column of Z,

[n, θ, s

] = f (i). (2)

When a new image arrives, we match it with the

most similar scene included in the map database. For

that purpose, we ﬁrst compute its descriptor z

and

calculate its Euclidean Distance d with all the descrip-

tors included in Z:

∑

a=1

i,a

− z

)

, i = 1. . . m. (3)

gives information about the appearance simi-

larity between an input image and all the images of

the map, and it is used as a classiﬁer. The algorithm

selects the Nearest Neighbor, and associates to d the

corresponding values of n, θ and s

of the retrieved

node’s image. We repeat this process for different

zooms of the route’s image. Then, we select the Near-

est Neighbor using again d as a classiﬁer between the

retrieved cases for each s

. This way, from each image

of the route we obtain the information vector:

[n d θ s

]. (4)

Up to this point, we have presented the matching

process between the node and the route images using

different scales from which we obtain a higher pre-

cision in the image retrieval and the relative position

of the images. Now, we continue describing the graph

creation process using the information included in (4).

The decision of adding a new node to the map in-

volves the lasts route retrieval image results. Specif-

ically, we study the previous ﬁve information vectors

included in the algorithm. First, we estimate the mode

of the nearest nodes, n

, included in these ﬁve infor-

mation vectors. Being M the number of times that n

appears in the last ﬁve image matchings, and µ and

σ the mean and standard deviation of all the d’s in-

cluded in the information vectors so far, a new node

is included in the graph if any of these two conditions

is achieved:

• M ≥ 3

• M = 2 and d

< µ − σ

When the information vector has a retrieval with

an associated image distance d > µ + 2σ, it is not

taken into account, since a high value of d indicates

low reliability in the association.

To estimate the topological relations between

nodes, we create the adjacency matrix A ∈ R

N×N

, be-

ing N the number of nodes. A is a sparse matrix with

rows labelled by graph nodes, with 1 denoting adja-

cent nodes, or 0 on the contrary.

Regarding the topological distance of the nodes in

the graph, we use the scale factors to determine it.

Being l

and l

the differences of scales of the ﬁrst

and last image of the route where the same node is

detected, the topological distance c between a node n

and n

i+1

is deﬁned as:

i,i+1

= l

− l

i+1

(5)

In order to build the graph, we also estimate the

relative orientation between nodes. θ

denotes the

orientation associated with the ﬁrst route image that

retrieves the node i, and θ

the orientation of the last

one before a new node is found. We assume that θ

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Figure 2: Example of two test images located in different relative positions regarding the closest node. (a) Image node 1, (a’)

Zoom-in of the Image Node 1, (b) Image Test 1, (c) Image Test 2, (c’) Zoom-in of the Image Test 2 and (d) Image Node 2. On

the right, it appears samples of the images (a), (a’) and (b) to show the zoom process and appearance similarity improvement.

and l

are topological distances between a node and a route image, and c the topological distance between nodes.

Figure 3: Phase change estimation in a node.

is the direction that the robot has to follow in order

to arrive to the next one. We estimate the phase lag

produced in a node as:

∆θ

= θ

− θ

(6)

In Fig. 3 we can see a graphical representation of

the phase change estimation in a node. We set the ori-

entation of the map by deﬁning the direction of the

output image for the ﬁrst node. That direction deﬁnes

the global orientation system of the map. After that,

the orientation of the graph is updated in every node

using ∆θ

. Although the map and the nodes use differ-

ent angle reference systems, it does not affect to the

results since we compute angle differences. Once we

have deﬁned the global map orientation reference, we

can compute the phase lag with each node local ori-

entation system. That information will be used during

the path estimation task.

When a new route is studied, the algorithm ini-

tializes a new coordinates system. That route will

be analyzed independently of the global graph until

a common node is found. Using the position and ori-

entation of the common node regarding both systems,

Map 1

Nodes

(a)

Map 2

Nodes

(b)

Figure 4: Graph representation of the node’s arrangement

obtained with the map building algorithm for (a) Area 1 and

(b) Area 2.

we are able to add the new nodes to the global graph

correctly. If the path of a new route coincides with a

previous one, the topological distance c of the nodes

is estimated again, and the result included in the map

by calculating the mean with the previous values.

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389

In Fig. 4 it is possible to see the map’s graph of (a)

the Area 1 and (b) the Area 2. In the experiments, we

use a high number of scales in order to increase the

precision in the topological distance estimation. In

particular, s

has a maximum value of 2.5 with a step

of 0.1, and s

reaches 1.4 with an increment of 0.05.

With that parameters, the time spent to make the nec-

essary comparisons per route image is 720 ms. We

can appreciate that the algorithm is able to estimate

the connections between nodes maintaining the ap-

pearance of the real layout of both areas. The Area 1

has been the most challenging due to the higher num-

ber of nodes, the transition from different rooms and

the loop in the map. The graph representation slightly

differs from the real layout, specially in the angle of

the right lower part nodes of the loop. Those nodes are

where the loop closure is produced, and the angle dif-

ference is due to the accumulated error in the distance

estimation of the nodes in the loop, not in the angle

estimation. Since the estimation of the phase lag be-

tween nodes is correct, the navigation is not affected

despite of the inaccuracy in the graph representation.

If there is not enough distance between adjacent

nodes, or the frequency of the route’s images is low,

a node might not be included in the graph, as the al-

gorithm does not ﬁnd the necessary repetitions of the

node in the information vector when doing the node

retrieval. The system is especially sensitive in the

phase lag between nodes, since it is based on the an-

gle estimation of the input and output node’s images.

For that reason, it is advisable to raise the frequency

of the image acquisition in the nodes where there is a

change in the direction.

4 PATH ESTIMATION

ALGORITHM

Once we obtain the graph of the map, our follow-

ing objective is to estimate the path of the routes in

the map. This can be faced as a localization prob-

lem using visual information. If we base the local-

ization of the route just on the retrieval of the nearest

node’s images, our knowledge of the positions will

be limited to node’s location. In these experiments

we try to improve the localization extending it also to

intermediate points between map nodes. We use the

scale analysis of the images to carry out this task in

a similar way as seen in section 3. The algorithm

uses the adjacency matrix A and the map database

Z that includes the descriptors of the node’s images

obtained during the map building. The comparison

of the global-appearance descriptor of a route image

with Z provides a measurement of their similar-

ity with all the node’s descriptors using (3). On the

other hand, the matrix A contains information about

the topological distance of the matched nodes, mak-

ing it possible to ﬁnd out the minimum topological

distance between two nodes of the map.

Once the descriptor z

of an image’s route has

been built, the ﬁrst step consists in calculating the

Euclidean distance between it and the descriptors in-

cluded in the map database (i.e., the descriptors of the

node’s images). We obtain d

for i = 1. . . m. We iden-

tify each d with its corresponding node n, angle θ and

node image scale s

. Then, we classify the results re-

garding d. We select the k-nearest-neighbors, and re-

peat the experiments for different route images scales

. Speciﬁcally, we use k = 10 neighbors.

Next, we weight the image distance d of every se-

lected neighbor using their position and orientation.

The aim is to penalize the probability of neighbors

that are geometrically far from the last robot pose.

Since our classiﬁer uses the minimum image distance

d as a criteria, we deﬁne a function that multiplies

the image distance of each neighbor regarding a fac-

tor that increases according to the topological distance

and phase lag.

To carry out this process, we ﬁrst estimate the

topological distance between the position of the pre-

vious route image and every neighbor selected dur-

ing the matching. We are able to ﬁnd out the shortest

path between two nodes using the information stored

in A. Since we have a connected graph, a path that

connects two nodes of the map can always be found.

Being c

n1,n2

the cost to traverse two adjacent nodes

, n

∈ A, and P

i, j

= [n

, . . . n

] the sequence of nodes

of the shortest path that connects n

and n

, the cost

i, j

associated with P

i, j

can be deﬁned as:

i, j

∑

i+1

(7)

being c

i+1

the topological distance between ad-

jacent nodes deﬁned in (5).

Our weighting function takes into account

changes in both position (nodes) and orientation.

Considering the image i−th of a route, the value of d

is updated as:

= d × [w

·C

i,i−1

+ w

· ∆θ

i,i−1

] (8)

and w

are weighting constants. Speciﬁcally,

is related with the topological distance, and w

weights changes in the path orientation. The function

updates the image distance d based on the topologi-

cal distance and phase lag between each neighbor and

the previous localization of the path. The multiplier

weighting term increases as the neighbors present

higher topological distance and orientation difference

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Map 1

Map

Route 1

(a)

Map 1

Map

Route 4

(b)

Map 1

Map

Route 6

(c)

Map 1

Map

Route 8

(d)

Map 2

Map

Route 1

(e)

Map 2

Map

Route 2

(f)

Map 2

Map

Route 3

(g)

Map 2

Map

Route 4

(h)

Figure 5: Path estimation of the (a) Route 1, (b) Route 4, (c) Route 6 and (d) Route 8 of the Area 1 over the created graph,

and path estimation of the (e) Route 1, (f) Route 2, (g) Route 3 and (h) Route 4 of the Area 2 over the created graph

regarding the last path location. By incrementing the

image distance of an experiment, we reduce its likeli-

hood of being chosen as nearest neighbor. That way,

the function penalizes important changes in position

and orientation between consecutive route scenes.

The multiplier term might change for each neighbor

of the current node, since the estimated nearest node

and orientation may vary in every particular case. We

determine the constants’ value experimentally. In our

function, we choose w

= 0.15 and w

= 0.1.

Once the image distances are updated, we classify

the selected experiments regarding d

, and choose the

Nearest Neighbor. As a result, we ﬁnd out the closest

node n to the route image, its orientation θ, and the

scales of both the node’s image s

and the route’s im-

age s

. We have to take into account that θ must be

corrected with the phase lag between the map global

system and the node reference system, estimated pre-

viously in the map building. The current position of

the robot in the graph is estimated using the nearest

node and the relative position with that node (l) using

(1).

Figure 5 shows the path estimation of different

routes of the two areas. The dots in the route’s paths

represent the position of the different images studied.

The values of s

and s

have been determined experi-

mentally, being 2.2 the maximum scale with a step of

0.4 and 0.3 respectively. The time necessary to carry

out the localization of an input image is 330 ms.

We can compare the results with the synthetic

routes path representation in Fig. 1. As it can be seen,

the algorithm deals with the interpolation of the lo-

cation estimation in halfway positions of the nodes

using the image’s scales information. In general, the

location precision in changes of direction in the routes

decreases. It is also important that, despite the fact

that we introduce the weighing function, the algo-

rithm is capable of ﬁnding again the correct position

although a previous estimation is not correct, as we

can see in Fig. 5(a) and (c). The result in the path rep-

resentation of the fourth route of Area 1 (Fig. 5(b)) is

also interesting. As we can appreciate in Fig. 1(b),

the route 4 presents a path that differs from the layout

of the nodes, and the algorithm is able to estimate the

position accurately despite that fact.

Therefore, the results prove that our algorithm

deals with the estimation of the route path in inter-

mediate positions of the nodes and also deals false

association in former experiments of the route despite

using a weighting function.

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5 CONCLUSIONS

In this paper we have studied the problem of topo-

logical map building and navigation using global-

appearance image descriptors. The map building al-

gorithm developed is able to estimate the relations be-

tween nodes and create a graph using the informa-

tion captured along some routes in the environment

to map. Moreover, we introduce a study of the im-

age’s scales in order to ﬁnd out the topological dis-

tance between nodes which can be considered to ap-

proximately be proportional to the geometrical dis-

tance. The results present a high accuracy in the node

detection and estimation of its adjacency and relative

orientation as it can be seen in the graphs obtained

in the map building process. All that information ar-

ranges the representation of the map through a graph.

We have also created an algorithm which esti-

mates the path of routes along the area. It takes proﬁt

of the image’s scale study to improve the location

with an interpolation of the route position between

nodes. The use of a weighting function to penalize

changes in position and orientation in consecutive im-

ages during the navigation improves the localization

accuracy. Despite that weight, the algorithm is able to

relocate the robot correctly although a previous image

of the route would introduce a false retrieval.

The results obtained both in the map building and

the path representation of routes encourage us to con-

tinue studying the possibilities of the application of

global-appearance image descriptors to topological

navigation tasks. It would be interesting to extend

this study in order to ﬁnd the minimum information

necessary to make the navigation optimal, the appli-

cation of new global-appearance descriptors, or the

improvement in the phase estimation in order to make

the algorithm able to correct small errors in the orien-

tation.

ACKNOWLEDGMENTS

This work has been supported by the Spanish gov-

ernment through the project DPI2010-15308.

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