Paraskevas Diamantatos
email: diamantatos@aegean.gr

Ergina Kavallieratou
email: kavallieratou@aegean.gr

Android Based Electronic Travel Aid System for Blind People

Keywords: Blind, navigation, mobile phone 1

Blindness is the condition of lacking visual perception due to physiological or neurological factors. Blind people do not have the full perception of the surrounding environment, though navigating, in an unknown environment or/and with obstacles on route, can be a very difficult task. In this paper, an information mobile system is presented, that acts as an electronic travel aid, and can guide a blind person through a route, inform him about imminent obstacles in his path and help him orientate himself. The current prototype consists of a mobile phone, and the developed application.

INTRODUCTION

It is absolutely crucial in our time to be able to help blind people move in urban environments effectively, with a simple, easy accessible, low cost system. According to existed research there are almost 40 million blind people [START_REF]Global Data on Visual Impairment[END_REF] that naturally use a simple cane, or a guide dog to help them move around. Both ways have disadvantages: a cane cannot detect obstacles further away than its height, and the guide dogs while more expensive, are not enough for all the blind people.

The majority of the suggested systems [START_REF]Official Blog: Speech-friendly textual directions from Google Maps[END_REF][3][START_REF] Benjamine | a laser cane for the blind[END_REF][START_REF] Nagarajan | Role of Object Identification in Sonification System for Visually Impaired[END_REF][START_REF] Shoval | NavBelt and the Guide-Cane [obstacle-avoidance systems for the blind and visually impaired[END_REF][START_REF] Apostolopoulos | Integrating Minimalistic Localization and Navigation for People with Visual Impairments[END_REF][START_REF] Manduchi | Blind guidance using mobile computer vision: a usability study[END_REF][START_REF] Bourbakis | Sensing surrounding 3-D space for navigation of the blind[END_REF] are often too expensive and unpractical in use, while most of the available navigation systems, cannot detect obstacles in a specific route, they simply give directions to the user for a point A to a point B [START_REF]Official Blog: Speech-friendly textual directions from Google Maps[END_REF]. The proposed system helps the user to move in the environment, detecting obstacles and finding the best path, in order to avoid them. It can give vocal instructions to the user, or use the mobiles vibration in order to give navigation instructions. It is also able to orientate the user, using military vocal orientations e.g. north 12 o'clock.

In the following section 1.1, a short description of previous work is given, while in section 2, the proposed system is described in detail. Finally, some comparison results and conclusion are mentioned in sections 3 and 4, respectively.

LITERATURE REVIEW

There are two major elements of the mobility problem that a Blind person has to deal with. First, the blind must sense obstacles in his environment and avoid them. The second problem, equally serious as the first, is the person navigation [3].

In the recent years a number of navigation system products became available to the public. Systems, like Google maps [START_REF]Official Blog: Speech-friendly textual directions from Google Maps[END_REF] , that offer navigation from a point A to a point B, and can also support voice interaction with the user, braille interface, and screen reader interface especially for blind people [START_REF]Official Blog: Speech-friendly textual directions from Google Maps[END_REF].While the navigation problem, seems to be a solved problem for outdoor navigation, mostly, due to the quality of the offered services and products to the public, the obstacle detection problem remains.

ETAs, Electronic Travel Aids, try to deal with this problem. ETAs development started at the mid 60's. Some of the most known applications include the LaserCane [START_REF] Benjamine | a laser cane for the blind[END_REF], which is a regular long cane with a built-in laser ranging system. The Mowat Sensor is an example of a pocket-sized device containing an ultrasonic air sonar system [START_REF] Nagarajan | Role of Object Identification in Sonification System for Visually Impaired[END_REF]. When it detects an obstacle, the device vibrates, thereby signaling to the user. Similar technology is used on NavBelt [START_REF] Shoval | NavBelt and the Guide-Cane [obstacle-avoidance systems for the blind and visually impaired[END_REF], a belt that utilizes an ultrasonic sonar system, and a guide cane, a cane that has a robot attached that also utilizes ultrasonic sonar system in order to guide the user.

While most of the ETAs try to address the obstacle detection problem, some ETAs try to provide navigation for indoor uncharted buildings. More specifically, Navatar [START_REF] Apostolopoulos | Integrating Minimalistic Localization and Navigation for People with Visual Impairments[END_REF] utilizes several sensors that can be found on modern smartphones like accelerometer and compass to determine the movement of the user in the space. It also takes a user input into account, e.g. if a user finds a door he can save it on the system. By this information, Navatar can determine the user's location inside a building [START_REF] Apostolopoulos | Integrating Minimalistic Localization and Navigation for People with Visual Impairments[END_REF]. Another system for indoor navigation is a case study from the school of engineering of University of California where a system was developed that utilizes mobile phone cameras and searches for specific markers on the walls [START_REF] Manduchi | Blind guidance using mobile computer vision: a usability study[END_REF].

A different approach for developing an ETA was used on tyflos system [START_REF] Bourbakis | Sensing surrounding 3-D space for navigation of the blind[END_REF]. This system uses stereoscopic cameras in order to detect the depth of obstacles in the user's route and notify the user through a vibration belt. The research problem of designing a better ETA is a tough one. Despite 50 years of effort, no one has been able to design an electronic device that can replace the long cane.

THE PROPOSED SYSTEM

An application was developed that makes use of an android mobile phone with cameras along with sensors that can be found on every android smartphone, like accelerometer and compass. By analyzing the image taken by the camera and creating a depth map it is possible to detect obstacles in the user's path and redirect him by a different route.

In order to achieve that, two consecutively photos are considered and their common points are located. Then the optical flow between them is established, allowing extracting the homography and the fundamental matrices. This step is important in order to rectify the images and transform them to stereo images. This step allows the creation of a depth map that contains any objects found, along with their relative position in space. Next the routing subsystems computes a route with no obstacles and notifies the user. In this section, all the mentioned modules of the proposed system (fig. 1) will be further analyzed.

The proposed system is able to help blind people to be orientated in their environment by informing them orally on the location they are staring: north, south, east, west and their combinations. It consists of a total of 12 subsystems, as it is presented in figure 1. The system was developed in the Android mobile platform, and it also requires the Opencv for android library.

The Camera subsystem is responsible to capture two sequential frames using the user's mobile phone camera. The output is two bmp images with resolution 352*288. Low resolution images are used in order to achieve lower computational time. Thus, the system can analyze the image in real time. In the prototype version, the two frames are shown side by side on the user's mobile phone screen, just for testing purposes.

The Points subsystem is responsible to identify common points between the two images acquired by the Camera subsystem, using a detector. Various detectors were tried, offered by opencv library for this task, like SURF [START_REF] Bay | SURF: Speeded Up Robust Features[END_REF]: a robust local feature detector that is based on sums of 2D Haar wavelet responses, ORB [START_REF] Rublee | ORB: an efficient alternative to SIFT or SURF[END_REF]: a very fast binary descriptor based on BRIEF, and GFTT [START_REF] Shi | Good Features to Track[END_REF]: a detector that finds the most prominent corners in the image. The results prooved that GFTT (good features to track) detector was ideal for the task, because of its very low computational time.

The Optical Flow subsystem is responsible to calculate the optical flow, i.e. the distance of the corresponding points (shift) between the first and the second frame, detected in the previous subsystem. It is absolutely crucial for the entire system that the points and optical flow subsystems return exact results, since all the next steps depend on those points and their optical flow.

The Fundamental subsystem, along with the Homography subsystem are responsible to calculate the fundamental [START_REF] Luong | The Fundamental Matrix: Theory, Algorithms, and Stability Analysis[END_REF] and the homography [START_REF] Hartley | Multiple view geometry in computer vision[END_REF] matrices, respectively. The fundamental matrix is a 3×3 matrix which relates the corresponding points in stereo images. While homography relates the transformation from a projective space to itself that maps straight lines to straight lines. Homography has many practical applications, such as image rectification, which our system performs on the Rectify subsystem. It is also used for image registration, or computation of camera motion (rotation and translation) between two images. Once camera rotation and translation have been extracted from an estimated homography matrix, this information may be used for navigation, or to insert models of 3D objects into an image or video, so that they are rendered with the correct perspective and appear to be part of the original scene.

The rectify subsystem is responsible to transform the two bmp images in stereoscopic images [START_REF] Holliman | 3D Display Systems[END_REF], images taken by a stereoscopic camera. Thus, their common points are located on the same axis. Opencv provides the tools for the image rectification process [START_REF] Dröppelmann | Stereo Vision using the OpenCV library[END_REF]. It is suggested that the rectification is made by using the camera characteristics along with the homography matrix. The problem here is that the camera characteristics are not available for every camera that someone can use in a mo-bile phone. However, the rectification is also possible by using only the homography matrix. The Depth Map subsystem is responsible to calculate the disparity depth map of the two stereo images of the rectify subsystem. A disparity depth map [START_REF] Dröppelmann | Stereo Vision using the OpenCV library[END_REF] is a 2D image where the color of each pixel represents the distance of that point from the camera. In more detail, light pixels are near and dark pixels are far. The disparity depth map will be used in order to identify obstacles near the user, for the calculation of the path that the user should follow. Block matching algorithms [START_REF] Dröppelmann | Stereo Vision using the OpenCV library[END_REF] offered by openCV were used, in order to produce the depth map.

The Distance subsystem is responsible to roughly calculate the distances of all the objects that can be found on the depth map. This was implemented by dividing the densities of the pixels from the depth map in 5 sub images. For objects very near to the camera (figure 2), are considered those with densities in the range of 220 -255. Respectively a rough estimation (figure 3) is done for all the other objects (near, far, very far, and extremely far). The Routing subsystem is responsible to calculate the area in the image (left, right or center) that includes the freest space. This is done by calculating the horizontal histograms on each of the images extracted by the Distance subsystem. After an iterative process, the area in the image with the freest space is localized. For example on figures 2 and 3, on the right side, the depth map of a scene is presented, while on the left only specific pixel densities are selected to be on. By considering the objects located very near (fig. 2, left image), and calculating the horizontal histogram of the left image, it is computed that on the left side of the scene, the user has free space to move, while on the right side of the scene, the user has no free space.

The Text-to-speech subsystem is responsible to notify the user with voice commands, while the Vibration subsystem, if selected, is responsible to notify the user with vibration codes. One vibration stands for left, two vibrations for right.

A Direction subsystem was also implemented that is responsible to notify the user of the direction he is headed, orally, using military codes. For example, if the user is headed north, the system will notify the user that he is headed at 12 O' clock.

COMPARISON RESULTS

Ιt ιs hard to actually measure the results, mostly because there is no standard evaluation technique. However, it is possible to check, if we get the expected results from the subsystems.

For the Optical Flow subsystem, that is based on the Points subsystem, it was possible to measure the detected distances of the points, manually. The followed procedure should save the 2 sequential frames, along with the points detected, and their optical flow. The extracted information for 20 different sets of frames was reviewed. The success rate of this subsystem was 85%, due to some misplaced points, that is a normal behavior for this kind of subsystem.

The Rectify subsystem that is based on the Fundemental and Homography subsystems is the one responsible for the bad output of our algorithm. The accuracy of this system was also measured manually. 50 rectified images were kept, and later reviewed. Only the rectified images onto a common image plane in such a way that the corresponding points have the same row coordinates, where considered to be the ones expected. Specifically only the 4 % of the frames work as expected, making things worse.

The Depth Map subsystem works as expected. Known datasets were used to test the performance of this subsystem, along with their ground truth data. By tuning the characteristics of this subsystem an identical image to the ground truth was achieved. A total of 20 sets of stereo images where used, to output their depth maps. Overall the success rate of this subsystem found to be 95%.

The results revealed that the depth map creation is exceptional. On figure 2 we can see a depth map created from our system on a monocamera device, while on figure 3 a depth map created from images taken from a stereoscopic camera device is presented. For the Routing subsystem that is based on the Distance subsystem several depth maps were used, and on each one of the depth maps, a decision was made over which direction the user should go. The success rate of our algorithm was 70%.

CONCLUSION

Although our system works in some frames, it is not the case for all of them. Thus, it cannot be used in a real time application. Responsible for that is the camera characteristics that are not available on most of the mobile phones. Usually mobile phone manufacturers do not care to have available any of the camera characteristics per device. They just care for the camera to work. This is making the development of such application, which utilizes only one camera, difficult, because it also requires a subsystem for camera calibration. Implementing one in our tests, different camera characteristics were extracted every time. Without camera characteristics, another function for camera calibration (stereoBM) was used that did not give so good results.

Although the final results are not perfectly good, and this system cannot be used by blind people yet, for safety reasons, we strongly believe that this kind of application is possible to be implemented in 3D mobile phones with 3D stereo cameras.

Fig. 1 .

 1 Fig.1. Overview of the proposed system.

Fig. 3 .

 3 Fig.3. Objects located extremely far. Depth Map on right, Left only pixel densities between 0-80 are on

Fig. 4 .Fig. 5 .

 45 Fig.4. Depth map from monocamera device


Anastasios Rigos
email: a.rigos@aegean.gr

Olympos P Andreadis
email: olympros@marine.aegean.gr

Manousakis Andreas

Michalis I Vousdoukas
email: vousdoukas@fzk.uni-hannover.dect10087@ct.aegean.gr

George E Tsekouras

Adonis Velegrakis
email: adonis.velegrakis@gmail.com

Shoreline Extraction from Coastal Images Using Chebyshev Polynomials and RBF Neural Networks

Keywords: Coastal morphodynamics, remote sensing, RBF neural networks, fuzzy clustering, steepest descent

In this study, we use a specialized coastal monitoring system for the test case of Faro beach (Portugal), and generate a database consisted of variance coastal images. The images are elaborated in terms of an empirical image thresholding procedure and the Chebyshev polynomials. The resulting polynomial coefficients constitute the input data, while the resulting thresholds the output data. We, then, use the above data set to train a radial basis function network structure with the aid of input-output fuzzy clustering and a steepest descent approach. The implementation of the RBF network leads to an effective detection and extraction of the shoreline of the beach under consideration.

Introduction

Monitoring of the shoreline position has become an issue of urgency given the high socio-economic value and population density of the coastal zone [START_REF] Goncalves | A comparison between three short-term shoreline prediction models[END_REF][START_REF] Huisman | The use of video imagery to analyse groundwater and shoreline dynamics on a dissipative beach[END_REF], the increasing erosion as well as the projected sea-level rise. Beach morphology is known to change in different spatial and temporal scales, a fact that requires intensive monitoring schemes while the energetic conditions make non-intrusive techniques very attractive [START_REF] Pearre | Quantifying seasonal shoreline variability at Rehoboth beach, Delaware, using automated imaging techniques[END_REF][START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF]. As a result, the application of coastal video monitoring has been increased during the last three decades [START_REF] Holman | The history and technical capabilities of Argus[END_REF][START_REF] Plant | The performance of shoreline detection model applied to video imaginary[END_REF] allowing non-intrusive, continuous measurements at temporal and spatial scales and resolutions for which in situ data collection would demand much greater than acceptable inputs of personnel, equipment, and cost. However, despite the application of coastal video monitoring systems for more than two decades still, developing a universal and robust automatic shoreline detection procedure remains a challenge, due to the variety of intra-annual environmental, hydrodynamic and morphological conditions at the coastal zone [START_REF] Plant | The performance of shoreline detection model applied to video imaginary[END_REF]. Against the foregoing background [START_REF] Madsen | Intertidal beach slope predictions compared to field data[END_REF][START_REF] Uunk | Automated mapping of the intertidal beach bathymetry from video images[END_REF], the present contribution aims to build a systematic methodology for coastal shoreline detection using radial basis function (RBF) artificial neural networks.

RBF networks have been exercised as efficient black-box techniques that have been implemented in a wide range of applications [START_REF] Filho | Visual RBF network design based on star coordinates[END_REF][START_REF] Er | High-speed face recognition based on discrete cosine transform and RBF neural networks[END_REF][START_REF] Pedrycz | Granular-oriented development of functional radial basis function neural networks[END_REF][START_REF] Roh | The design methodology of radial basis function neural networks based on fuzzy K-nearest neighbors approach[END_REF][START_REF] Filho | Visual RBF network design based on star coordinates[END_REF][START_REF] Er | High-speed face recognition based on discrete cosine transform and RBF neural networks[END_REF]. The training process is based on estimating three kinds of parameters: the neuron centers and widths, and the connecting weights between neurons. The estimation of the centers is carried out through cluster analysis; the corresponding widths are evaluated in terms of the above centers, and finally the connection weights using least squares or gradient descent.

In this paper, we present an automated methodology for the shoreline extraction from coastal grayscale variance images. The proposed methodology encompasses three modules. The first module performs an empirical image thresholding process. The second module employs the Chebyshev polynomials [START_REF] Mason | Chebyshev Polynomials[END_REF][START_REF] Rivlin | The Chebyshev Polynomials[END_REF] to approximate the histograms of the resulting images. Finally, the third module applies an RBF network, which is trained in terms of input-output fuzzy clustering and a steepest descent approach based on Armijo's rule [START_REF] Armijo | Minimization of functions having Lipschitz continuous first partial derivatives[END_REF]. The result is an integrated system able to accurately detect and extract the shorelines.

The rest of the paper is synthesized as follows: Section 2 describes the location of interest and the monitoring system. Section 3 presents the proposed methodology in details. The experimental results are provided in Section 4. Finally, the paper concludes in Section 5.

Study Area and Monitoring System

The study area is the Faro Beach (Praia de Faro) located along the central and eastern parts of the Ancão Peninsula, in the westernmost sector of the Ria Formosa barrier island system in Portugal. Tides in the area are semi-diurnal, with average ranges of 2.8 meters (m) for spring tides and 1.3 m for neap tides although a maximum range of 3.5 m can be reached [START_REF] Vousdoukas | Coastal vulnerability assessment based on video wave run-up observations at a meso-tidal, reflective beach[END_REF]. Faro Beach is a 'reflective' beach [START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF] with beach-face slopes typically over 10% and varying from 6% to 15%, and a tendency to decrease eastwards, where a 'low tide terrace' beach state is found [START_REF] Vousdoukas | Coastal vulnerability assessment based on video wave run-up observations at a meso-tidal, reflective beach[END_REF]. Beach sediments are medium to very coarse sands with d50~0.5 mm and d90~2 mm. Coastal imagery was provided by a coastal video [START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF] consisting of two Mobotix M22, 3.1 megapixel (2048 x 1536 resolution), Internet Protocol (IP) cameras, installed on a metallic structure, placed on the roof of a restaurant in Faro Beach, and connected to a PC. The elevation of the centre of view (COV) is around 20 m above mean sea level (MSL). The image acquisition took place at 1 Hz, at hourly 10 min bursts, during daylight. After each 10 minutes image acquisition set, the system was scheduled to run processing scripts which generate the 'primary products', i.e. snapshot images, time averaged (TIMEX) images, variance images, and timestack images [START_REF] Holman | The history and technical capabilities of Argus[END_REF].

The Proposed Methodology

In this study, we obtain grayscale variance images of the coastal line, commonly called SIGMA images [START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF][START_REF] Vousdoukas | Coastal vulnerability assessment based on video wave run-up observations at a meso-tidal, reflective beach[END_REF]. These images represent the sum of the absolute pixel intensity differences between consecutive images and can be considered as 'accumulated motion images'. Using the above monitoring system, we generated 1600 SIGMA images for various angle view positions of the camera. Fig. 1(a) depicts a typical SIGMA image, where high intensity values are related to high wavebreaking and swash activity. The corresponding normalized histogram is given in Fig. 1(b).

The proposed method consists of three steps aiming towards developing a fully automated methodology able to exhibit accurate shoreline detection and extraction. The first two steps generate the input data and the output data, and the third one uses the above data to train the RBF network.

Histogram Approximation Using Chebyshev Polynomials

In this step we generate the input data used by the RBF network. Specifically, we attempt to approximate the histogram of each SIGMA image using Chebyshev polynomials, where each polynomial coefficient defines one and only one dimension of the input space of the RBF network. Thus, the number of polynomial coefficients defines the dimension of the network's input space. This fact justifies our choice to use the Chebyshev polynomials because they constitute orthogonal polynomials and they possess and inherent ability to exhibit high approximation accuracy by utilizing a small number of coefficients. Eventually, the input space dimension is kept within reasonable levels. According to Weierstrass's theorem [START_REF] Rivlin | The Chebyshev Polynomials[END_REF] every continuous function ( ) f x on a closed interval can be approximated as closely as desired by a polynomial function 0 ( ) ( )

r p p p f x c T x = = ∑  (1) (a) (b)
where

( ) f x  is the approximation of ( ) f x , r is the polynomial's order, (1 )
p c p r
≤ ≤ are the polynomial coefficients, and ( ) p T x is a continuous polynomial of order p . The order r is chosen as to approximate the following error function,

{ }

min max ( ) ( )

error J f x f x = - (2)
In what follows, we shall consider one-dimensional space, which is also our case since the histogram distributions of the SIGMA images are one-dimensional.

The Chebyshev polynomial of order r can be written as follows [START_REF] Rivlin | The Chebyshev Polynomials[END_REF],

( ) [ ] [ ] /2 /2 2 0 ( ) cos 1 2 r r p r k r p j p r j T x r x j k θ - = =      = = -             ∑ ∑ (3) with cos . x θ = The Chebyshev polynomials are orthogonal in [ ] 1, 1 - with respect to the subsequent weighting function, 2 1 ( ) 1 h x x = - (4)
The orthogonality is defined according the to the following relationship,

1 1 0, ( ), ( ) ( ) ( ) ( ) , p q p q p p q T x T x h x T x T x dx p q λ - ≠   = =  =   ∫ (5)
where ⋅ stands for the inner product and, ( )

1 2 1 , 0 ( ), ( ) ( ) ( ) / 2, 1, 2,..., p p q p p T x T x h x T x dx p r π λ π - =  = = =  =  ∫ (6)
The polynomial coefficients of the function expansion in (1) can be written as,

1 1 , 1 ( ) ( ) ( ) , p p p p p p f T c h x f x T x dx T T λ - = = ∫ (7) with 1, 2,..., . p r =
The orthogonality implies that the polynomial functions do not overlap with each other. It thus appears that each coefficient k c can be adjusted without causing any side effects to the rest of coefficients, meaning that they are independent each other. This is the property we wanted to obtain in the first place because, in our approach, the polynomial coefficients define the input space dimensions.

Since our data are discrete, the discretization of the above inner product relationship can be obtained by implementing the Forsythe's algorithm [START_REF] Mason | Chebyshev Polynomials[END_REF]. This method assumes a set { } 1

;

N k k k x y = of input-output data with [ ] 1, 1 k
x ∈and minimizes the error function in eq. ( 2) by using a monic polynomial of the form, 0 ( )

1 k t x = , 1 ( ) k k t x x = , 2 1 0 1 ( ) ( ) ( ) 2 k k k k t x x t x t x = - (8) 1 2 1 ( ) ( ) ( ) ( 2) 4 r k k r k r k t x x t x t x r - - = - > (9)
To this end, the Forsythe's algorithm modifies the equation ( 7) and states that the best fitting of the available discrete data set is obtained if the polynomial coefficients are calculated according to the subsequent formula, ( )

1 2 1 ( ) ( ) ( ) ( ) N k k p k k p N k p k k h x y t x c h x t x = = = ∑ ∑ (10)

Image Thresholding

In this step, we generate the output data. To accomplish this task, we employ the thresholding process developed in [START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF]. The basic issue of this approach is to normalize the pixel intensities as follows: , , max ˆi j i j j

I I I = (11)
where , i j I is the pixel original intensity, where 1 i M ≤ ≤ and 1 j N ≤ ≤ indicate horizontal and vertical pixel dimensions, respectively, of an image of size M N × pixels. The quantity max j I corresponds to the smoothed alongshore pixel intensity maxima vector. Given that a standard region of interest was considered, the only input parameter for the shoreline detection model was the pixel intensity threshold ˆthr I , which has been shown to be related to the pixel intensity histograms. The interested reader can find a detailed presentation of the thresholding approach in [START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF].

Training Process of the RBF Network

Based on the above process, the data set to train the network is formulated as follows:

( ) [ ] { } 1 2 , : , ,..., , , 1
T k IO k k k k k kr k thr S y c c c y I k Q = = = ≤ ≤ x x ( 12
)
where Q is the number of the training data, r is the order of the Chebyshev polynomial which coincides with the input space dimension and is the same for all images, and kj c (1 ) j r ≤ ≤ are the polynomial coefficients. Notice that 1600 Q <

. In order to train the RBF network we must determine effective input-output relationships, which are provided by an optimal set of values of the network's parameters. The most crucial issue is the determination of the radial basis function centers. Fuzzy cluster analysis has been intensively involved in deciding appropriate values for those parameters. In this paper, we employ the algorithm developed by Pedrycz in [START_REF] Pedrycz | Conditional fuzzy clustering in the design of radial basis function neural networks[END_REF], which is based on the implementation of the fuzzy c-means. The algorithm performs a separate fuzzy clustering in the output space. The number of clusters defines the number of contexts in the input space. The input data belonging to the same context correspond to the output data that belong to the same cluster in the output space. Then, a separate conditional cluster analysis is implemented with respect to each context, where all contexts are partitioned into the same number of clusters. In both clustering schemes the fuzziness parameter was selected to be equal to 2. To this end, the form of the radial basis function is,

2 1 ( ) 1 n k i i k j k j g =   -   =   -   ∑ x v x x v ( 13
)
where n is the number of hidden nodes (i.e. radial basis functions), and

r i ∈ ℜ v
the center of the i-th basis function. The interested reader can find a detailed presentation of this algorithm in [START_REF] Pedrycz | Conditional fuzzy clustering in the design of radial basis function neural networks[END_REF]. The estimated network's output is, 1 ( )

n k i i k i y w g = = ∑ x  (1 ) k Q ≤ ≤ (14)
with i w being the connection weight of the i-th hidden node. Notice that the above basis function does not use any width parameter, since this parameter has been absorbed by the radial basis function form.

The connection weights are calculated by a steepest descent approach, which is based on Armijo's rule [START_REF] Armijo | Minimization of functions having Lipschitz continuous first partial derivatives[END_REF]. The objective is to minimize the network's square error,

2 1 Q SE k k k J y y = = - ∑  (15)
Then, for the 1 t + iteration, (

) SE t t t J t α + = - ∇ w w w 1) ( ) ( ) ( ( )
...

T n w w w = w and, 1 2 ( ) , ,...,
T SE SE SE SE n J J J J w w w   ∂ ∂ ∂ ∇ =   ∂ ∂ ∂   w ( 17
)
The partial derivatives in (

( )

n SE k k i k k i J y y f w = ∂ = - - ∂ ∑ x ( 18
)
The parameter ( )

t α in (16) is: ( ) t µ α β = (19) where (0,1) β ∈
. The parameter µ is the smallest positive integer such that, (

) SE SE SE SE J t a t J t J t a t J t ε - ∇ - < - ∇ w w w w ) ( ) 2 ( ) ( ) ( ( )) ( ) ( ) ( ( )
.

Experimental Study

The data set consists of 1600 SIGMA images and therefore the available data set includes 1600 L = data. The first experiment concerns the approximation of the image histograms by the Chebyshev polynomials. To perform the experiment we used 200 N = discrete intensity levels. Thus, for each image, the Chebyshev polynomials were used to fit 200 image data. The approximation accuracy was evaluated in terms of the root mean square error, that as the number of coefficients (i.e. the polynomial degree) increases so does the approximation accuracy. This fact is strongly supported by Table 1, where the mean values of the RMSE along with the respective standard deviations for all the 1600 SIGMA images are reported.

Fig. 3. Shoreline extraction for two different SIGMA images taken from Faro beach using the proposed RBF neural network and the Otsu's method [START_REF] Vousdoukas | Coastal vulnerability assessment based on video wave run-up observations at a meso-tidal, reflective beach[END_REF]. 1, the differences are not too large. Based on the last remark, and since the number of polynomial coefficients define the dimensionality of the network's, which must be kept within reasonable levels, we choose to use approximations obtained by the Chebyshev polynomials of degree equal to 6 r = . Therefore, in this experimental case, the input space dimension of the RBF network is equal to 7. The performance index (PI) used to evaluate the network is,

SE PI J Q = (22)
To train the network we divided the available 1600 data into 960 Q = training data (i.e. 60%), while the rest 640 (i.e. 40%) as testing data. In addition, the proposed method is compared to the well-known Otsu's image thresholding algorithm [START_REF] Otsu | A threshold selection method from gray-level histograms[END_REF]. Fig. 3 illustrates the shoreline extractions of two different SIGMA images obtained by the proposed method and Otsu's algorithm. To obtain this figure we used a RBF network with 8 n = hidden nodes. According to this figure our approach significantly outperformed the other method. This result is strongly evident in Table 2, which presents a simulation comparison in terms of the mean values of the PI and the corresponding standard deviations. To further evaluate our method, we used a data set coming from Ammoudara beach, which is located to the city of Heraklion at the northern coast of Crete (Greece). We used exactly the same RBF network that was trained by the data set from Faro beach. That is to say, the data set form Ammoudara beach are used all as testing data and the network had exactly the same parameter values as in the case of Faro beach. Again we compared our network with Otsu's method [START_REF] Otsu | A threshold selection method from gray-level histograms[END_REF]. The results of this experimental case are reported in Fig. [START_REF] Vousdoukas | Performance of intertidal topography video monitoring of a meso-tidal reflective beach in South Portugal[END_REF] and Table 3. According to those results, our network performed remarkably well, although the data set was "unknown" to it. Finally, similarly to the previous case, we can easily verify the superior behavior of the proposed method.

Conclusions

In this paper we have investigated the efforts to assess and enhance the automatic shoreline detection from images representing the sum of the absolute pixel intensity differences between consecutive images, obtained by a specialized monitoring system. The approach was exclusively carried out in terms of a sophisticated radial basis function neural network structure, which was trained by a fuzzy clustering scheme.

The experimental findings showed an effective performance with respect to the shoreline detection and extraction.

Fig. 1 .

 1 Fig. 1. (a) Typical SIGMA image and (b) the corresponding histogram.

Fig. 2 .

 2 Fig. 2. Histogram approximations using Chebyshev polynomials with degrees equal to: (a) 20 r = and (b) 6 r = .

  histogram frequency function and  ( ) l fr I the approximated one, which is provided by the expansion in eq. (1). Fig. 2 depicts the approximations of two different images with two different polynomial degrees. Notice (a) (b)

Fig. 4 .

 4 Fig. 4. Shoreline extraction for two different SIGMA images taken from Ammoudara beach using the proposed RBF neural network and the Otsu's method.

Table 1 .

 1 Mean RMSE values and the corresponding standard deviations of the histogram approximations for various polynomial degrees.

	Polynomial Degree	RMSE±Standard Deviation
	6	0.4354± 0.1072
	10	0.4035±0.1138
	14	0.3899±0.0933
	18	0.3746±0.0866

Table 2 .

 2 Comparative results in terms of the PI.

		No. of	Training	Testing
		Hidden Nodes	data	Data
	Proposed	6	0.0993±0.0036	0.0989±0.0300
	Method	8	0.0963±0.0036	0.0967±0.0303
		10	0.0907±0.0036	0.0946±0.0308
		12	0.0863±0.0035	0.0914±0.0312
	Otsu's Model		0.1631±0.01353
	However, in Table

Table 3 .

 3 Comparative results in terms of the PI.

		No. of	Training	Testing
		Hidden Nodes	data	Data
	Proposed	6	0.1104±0.0058	0.1298±0.0444
	Method	8	0.1081± 0.0122	0.1277±0.0388
		10	0.1004±0.0091	0.1248±0.0202
		12	0.0986±0.0066	0.1197±0.0456
	Otsu's Model		0.1831±0.00998

Acknowledgments. This research has been co-financed by the European Union (European Social Fund -ESF) and Greek national funds through the Operational Program "Education and Lifelong Learning" of the National Strategic Reference Framework (NSRF) -Research Funding Program: THALES. Investing in knowledge society through the European Social Fund.


Rudolf Schraml

Andreas Uhl

Similarity Based Cross-Section Segmentation in Rough Log End Images

Keywords: Wood imaging, Cross-section analysis, Cross-section segmentation, Rough log end images 2

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

In case of digital images of log ends there exist just a few publications which deal with cross-section (CS) analysis. The works of [START_REF] Wu | A computer vision method for detection of external log cracks and pith in log cross-section images[END_REF], [START_REF] Hanning | Determining the average annual ring width on the front side of lumber[END_REF], [START_REF] Österberg | Method for analyzing and classifying wood quality through local 2d-spectrum of digital log end images[END_REF], [START_REF] Norell | Estimation of pith position in untreated log ends in sawmill environments[END_REF], [START_REF] Schraml | Pith estimation on rough log end images using local fourier spectrum analysis[END_REF] present approaches for pith estimation and in [START_REF] Hanning | Determining the average annual ring width on the front side of lumber[END_REF], [START_REF] Cerda | Robust tree-ring detection[END_REF], [START_REF] Norell | An automatic method for counting annual rings in noisy sawmill images[END_REF], [START_REF] Norell | Counting annual rings on pinus sylvestris end faces in sawmill industry[END_REF] annual ring analysis approaches are proposed. Present CS analysis literature focuses on computed tomography (CT) cross-section images. Compared to conventional log end images, CT crosssection images do not exhibit disturbances due to cutting or dirt. Furthermore, the wood properties are clearly visible and distinguishable. This enables segmentation of the entire CS and of wood properties/ defects using basic thresholding techniques (literature review see [START_REF] Longuetaud | Automatic knot detection and measurements from x-ray ct images of wood: A review and validation of an improved algorithm on softwood samples[END_REF]). To our knowledge, no publications related to cross-section segmentation in digital images of rough log ends were published. Digital images of rough log ends can be taken at little cost and at almost every stage in the wood processing chain. The location, size and shape of the CS are crucial to perform sophisticated image analysis tasks. Thus, segmentation is a prerequisite for the development of novel applications (e.g. automated log grading or biometric traceability of logs -see [START_REF] Schraml | Temporal and longitudinal variances in wood log crosssection image analysis[END_REF]) using images of rough log end faces. Beneath a high segmentation accuracy, the timing performance of any segmentation approach is crucial for any real world application. Basically, a cross-section is built up of an annual ring texture which varies strongly locally. Variations are caused by the the circular alignment, dierent widths, colour features and disturbances of annual rings. Hence, CS segmentation is a typical task for region-based segmentation approaches which are able to segment textured regions. State-of-the-art region-based segmentation approaches are based on graph cuts ( [START_REF] Boykov | Interactive graph cuts for optimal boundary & region segmentation of objects in n-d images[END_REF], [START_REF] Boykov | Graph cuts and ecient n-d image segmentation[END_REF]), active contours ( [START_REF] Chan | Active contours without edges[END_REF], [START_REF] Chan | Histogram based segmentation using wasserstein distances[END_REF]) or mean shift ( [START_REF] Comaniciu | Mean shift: a robust approach toward feature space analysis[END_REF]) algorithms. In the past two decades manifold publications showed up high level segmentation algorithms combined with well matured texture features like Markov-random-eld statistics ( [START_REF] Haindl | Unsupervised texture segmentation using multiple segmenters strategy[END_REF]), Wavelet features ( [START_REF] Unser | Texture classication and segmentation using wavelet frames[END_REF], [START_REF] Wang | Supervised texture segmentation using wavelet transform[END_REF]), Gabor lters ( [START_REF] Weldon | Ecient gabor lter design for texture segmentation[END_REF]) and Fractal features ( [START_REF] Eiterer | Postal envelope address block location by fractalbased approach[END_REF]). Furthermore, there exist many more textural spectral-temporal features (literature review see [START_REF] Materka | Texture analysis methods -a review[END_REF]) and various new texture features and extensions were published (e.g. [START_REF] De Oliveira Nunes | Texture segmentation considering multiband, multiresolution and ane invariant roughness[END_REF], [START_REF] Stitou | Three-dimensional textured image blocks model based on wold decomposition[END_REF], [START_REF] Eckley | Locally stationary wavelet elds with application to the modelling and analysis of image texture[END_REF], [START_REF] Atto | 2-d wavelet packet spectrum for texture analysis[END_REF]).

Recently, in [START_REF] Jung | Texture segmentation via non-local nonparametric active contours[END_REF], [START_REF] Jung | Nonlocal active contours[END_REF] the region-based active contour approach proposed by [START_REF] Chan | Histogram based segmentation using wasserstein distances[END_REF] is extended to deal with similarity of adjacent patches which enables segmentation of inhomogeneous textured regions. This approach is applicable to CS segmentation, but requires a high computational eort. For this rst work dealing with CS segmentation we pay attention to the timing performance. Instead of using active contours we utilize an ease and fast computable region-growing approach which is based on similarity of adjacent patches. Similarity is assessed by comparing the histogram distances of texture features. For this purpose two fast computable features are evaluated as texture features: Intensity-and local binary pattern (LBP) histograms. The utilized region-growing approach can be combined with any comparable texture feature.

This work contributes to the development of new CS analysis applications suggesting a simple, accurate and fast computable approach for CS segmentation in rough log end images. A testset consisting of 108 dierent rough log end images is utilized to perform experiments. Results show that for the utilized algorithm simple intensity histograms as texture features and the earth movers distance (EMD) outperform a well-matured texture descriptor -the LBP operator. Additionally, the experiments examine dierent settings and parameters required for the segmentation algorithm.

At rst, Section 2 introduces the utilized texture analysis methods. In Section 3 the region-growing based CS segmentation algorithm is outlined. The experimental setup and results are presented in Section 4 followed by the conclusion in Section 5.

Local Binary Patterns (LBPs) were introduced by [START_REF] Ojala | A comparative study of texture measures with classication based on featured distributions[END_REF]. In counting the frequency of micro texels in an image or image section, LBPs unify statistical and structural principles of texture analysis. For each pixel in an image or image section the local binary pattern is computed by analysing N neighbours in a circular neighbourhood. The occurrence of each of the 2 N possible patterns is stored into a feature histogram, where each bin represents a single pattern and its frequency. Additionally to the generic formulation of the LBP operator, the authors of [START_REF] Ojala | Multiresolution gray-scale and rotation invariant texture classication with local binary patterns[END_REF] and [START_REF] Mäenpää | The Local Binary Pattern Approach to Texture Analysis -Extensions and Applications[END_REF] introduced uniform, rotation invariant and multi-scale LBP variations.

Histogram Distances are used as similarity measures between feature histograms of adjacent image sections. Four bin-by-bin distances (L1-Norm -L 1 , L2-Norm -L 2 , Chi-quadrat distance -X 2 , Hellinger distance -H) and one crossbin distance (EMD) are examined. The EMD [START_REF] Rubner | A metric for distributions with applications to image databases[END_REF] computes the minimal cost required to transform one histogram (P) into another (Q). In case of two onedimensional probability distribution functions P and Q the EMD is simply given by the L 1 norm between their cumulative distribution functions.

3

Cross-section segmentation algorithm

Our algorithm is inspired by the EMD-region-based level set formulation in [START_REF] Chan | Histogram based segmentation using wasserstein distances[END_REF], [START_REF] Jung | Nonlocal active contours[END_REF] and is adopted to a region growing procedure. The procedure is based on similarity of adjacent image sections. For this purpose, the image is subdivided into blocks. The block size and the overlapping factor between the blocks are crucial parameters which strongly inuence the segmentation accuracy and timing performance. Our algorithm is subdivided into three consecutive stages which are described subsequently.

Cluster initialisation

For the selection of seed blocks and the subsequent initialisation of clusters the position of the pith is utilized. We utilize the suggested algorithm and conguration presented in [START_REF] Schraml | Pith estimation on rough log end images using local fourier spectrum analysis[END_REF]. This pith estimation algorithm computes local orientations in the Fourier Spectra of image sections. The pith position is determined by intersection of the local orientations.

A predened number of blocks (e.g. 4) which are equally distributed close around the pith position are selected. Subsequently, for each single seed block the adjacent neighbours in a four-neighbourhood are added and then initialised as a single cluster.

Each cluster is initialised by computing three features which describe the contained texture: mean gray value/variance, mean entropy/variance and mean intensity histogram or LBP histogram distances between the blocks of the cluster and the corresponding variance.

Growing procedure

The cluster growing procedure starts with the selection of one of the initialised clusters. Then the four-neighbourhood of each border block is analysed. Only neighbours which are not allocated to a cluster are used as candidate blocks.Each candidate block is compared to the cluster which leads to a decision whether or not the block is allocated to the cluster. In Fig. 1 the blocks of a cluster and the decision making procedure are illustrated. For the block labelled B3 three candidate blocks (nb1, nb2, nb3) are available. The nal decision whether one of the candidates (e.g. nb2) is allocated requires that each of the three comparisons satises predened conditions. For example, the mean gray value of the block must range between the cluster mean gray value +/its variance. The feature-variances are used to regulate the restrictiveness of the decision making procedure. For this purpose, the variance is multiplied by a factor ranging from [-2,2]. Preliminary tests showed that other factors are either too restrictive or too tolerant for the growing procedure. If the block is allocated to the cluster, the cluster features are updated. The procedure continues with the next border block until no border block has further candidate blocks that t to the cluster. Then the algorithm continues with the next cluster. The cluster-growing algorithm nishes after all clusters are processed. Finally, the clusters are merged and it is assumed that the merged cluster represents the area of the CS. Cluster initialisation/growing/merging result using 16x16 half-overlapping pixels blocks An exemplary result is shown in Fig. 2 . It is clearly visible that the resulting cluster covers the entire CS. Unfortunately, similar textured CSs in the background are dicult to distinguish from the main CS. This problem is visible in the bottom right of Fig. 2 .

In three consecutive steps the nal estimate of the CS boundary is computed. First, all cluster blocks which have at least one neighbour that is not in the cluster are selected (see Fig. 3a). This step reduces the amount of blocks and all of the blocks representing parts of the CS boundary still remain. In the second step, it is assumed that CSs are approximately elliptical. First, a circle is tted into the point cloud of the remaining blocks. Blocks within the circle are removed. This improves the accuracy of the ellipse tting procedure. After ellipse tting all blocks located outside of the ellipse are removed (see Fig. 3b). In the best case and especially for elliptical CSs this procedure decreases the probability of including incorrectly segmented blocks (e.g. caused by neighboured CSs in the background). Finally, the alpha shape [START_REF] Edelsbrunner | On the shape of a set of points in the plane[END_REF] of all remaining blocks is computed. Alpha shapes are an approach to compute concave hulls and are a generalisation of convex hulls. They can be tuned by the α parameter. The higher the α value is, the better the alpha shape approximates the convex hull and details of the boundary are neglected. The lower the value of α is, the more details are considered. In contrast, a lower value makes the alpha shape computation vulnerable to large gaps between the outermost blocks. Finally, the alpha shape (see Fig. 3c) is used as a nal estimate of the CS boundary. and the deviation (StDev) across all of the 108 images. R describes the span between the minimum and the maximum of the computed segmentation accuracies. Additionally, the computation time in milliseconds [ms] provides information on the timing performance. The percentage of dierence between the pixels of the manually determined ground-truth mask (Fig. 4b) and the computed CS mask (Fig. 4c) is dened as the segmentation accuracy. All steps of the CS segmentation algorithm have been implemented in Java and all experiments have been performed on an Intel Core i7-2620M processor with 2.7 GHZ and 8 GB RAM, JRE 1.7.

Experiment #1 Intensity histograms

First, the applicability of intensity histograms as texture features for our algorithm is evaluated. Furthermore, block sizes of 16x16 and 32x32, half-and non-overlapping and all histogram distances noticed in Section 2 are examined.

For the cluster growing procedure each histogram distance is tested with variance factors (V f ) in a range between [-2.0,2.0]. For the entropy and mean gray value comparisons a constant V f = 1 is used. The circle/ellipse t step is not performed. The best results for all tested congurations are presented in Table 1. For three of four congurations the EMD achieves the best segmentation accuracy. The most accurate results are reached with EMD and 16x16 halfoverlapping pixels blocks (Mean: 5.55, StDev: 3.3). It can be stated that the EMD is a robust and appropriate histogram distance for all tested congurations. Results show that smaller block sizes and overlapping blocks increase the segmentation accuracy. Especially for shape estimation, a smaller distance between the block-center points leads to a renement and increases the accuracy of the CS boundary estimation. On the other hand, the amount of blocks is a crucial factor for the timing performance. With an increasing amount of blocks the timing performance decreases signicantly. For example, compare the nonand half-overlapping timing measurements in Table 1 .

Blocksize 16x16

H d V f Mean StDev R [
Furthermore, the results show that for non-overlapping blocks lower variance factors (V f ) and for half-overlapping blocks higher variance factors are required.

Overlapping and smaller blocks are more similar than larger sized ones which are not overlapping. Thus, the variance factors for larger sized blocks need to be higher and consequently less restrictive. Smaller block sizes and overlapping blocks require lower variance factors and enable a more accurate segmentation. Nearly all of the most accurate results for a certain conguration are computed using the L 2 norm. Contrary to the rst experiment, smaller blocksizes and overlapping blocks do not increase the segmentation accuracy. Due to strongly varying accuracies over all results it is not possible to draw further conclusions about the impact of the blocksize and half-/ non-overlapping blocks on the accuracy.

The most accurate result is achieved using the L 1 norm and multiscale & uniform LBPs (L 1 / 32x32/ half-overlapping Mean: 7.53, StDev: 3.41). It is dicult to conclude that using multiscale LBPs or uniform LBPs instead of normal 3x3 LBPs improves the segmentation accuracy. However, the two most accurate results are reached with the LBP extensions and especially with multiscale & uniform LBPs.

Results show that the two LBP extensions inuence the timing performance dierently. While for uniform LBPs the number of bins in the LBP histogram decreases, for multiscale LBPs the number of bins increases with each scale. Consequently, uniform LBPs increase the timing performance and multiscale LBPs cause a signicant deterioration of the timing performance.

The most important conclusion is that the results of the rst experiment are more robust over all congurations and histogram distances. The best results of the rst experiment using intensity histograms remarkable outperform the segmentation accuracies and timing measurements of the second experiment using LBP histograms. For evaluation of the timing performance, the testset images were scaled in a range from {0.1, 0.2, ..., 1, ..., 2} according to the amount of pixels. For each scale, the segmentation accuracies and timings are computed as described in Experiment #1 using EMD and half-overlapping blocks. The most accurate results for each scale and blocksize are used to illustrate the timing performance in Fig. 5.

Experiment #3 -Circle/ellipse tting

Compared to 32x32 blocks, with 16x16 blocks the amount of analysed blocks increases approximately by a factor of 4. Results show, that the timings for 32x32 blocks increase roughly linearly. The dierent increase of the 16x16 timings is caused by the Alpha shape computation step which has a complexity of O(nlogn). In case of 16x16 blocks and larger scales, the number of points used for Alpha shape computation increases rapidly. Thus, the impact on the timing performance becomes clearly visible. Finally, it can be stated that an appropriate selection of the blocksize is crucial for the timing performance and the accuracy of the CS segmentation algorithm.

Conclusion

We proposed a similarity-based region growing algorithm which is suitable for segmentation of CS in images of rough log end faces. In combination with intensity histograms as texture features and the EMD as histogram distance our algorithm is fast, accurate and robust. Surprisingly, LBP histograms as texture features achieve less accurate and very irregular results. Additionally, the timing performance decreases remarkable. These observations lead to an interesting conclusion. For particular segmentation applications, simple texture features and a more sophisticated similarity measure can outperform matured texture features and a simple similarity measure.

The experimental evaluation of our work forms a solid basis for further research on CS segmentation. In our future research further segmentation techniques will be evaluated based on their accuracy and timing performance. Apart

Fig. 1 .

 1 Fig. 1. Illustration of the cluster growing procedure

Fig. 2 .

 2 Fig. 2.

Fig. 3 .

 3 Fig. 3. Cross-section (CS) boundary estimation

4 Fig. 4 .

 44 Fig.4. Segmentation accuracy computation masks with a digital camera (Samsung WB2000), without ash and at approximately the same distance from the log end surface to the camera. The images were converted to grayscale using equal weighting factors. The accuracy for a certain conguration is evaluated computing the mean segmentation accuracy (Mean)

Fig. 5 .

 5 Fig. 5. Timing performance

Table 1 .

 1 Experiment #1 -Statistical analyisis

		ms]	H d	Blocksize 32x32 V f Mean StDev R [ms]
	L1 L2 H X 2	non-overlapping 0.9 7.29 3.74 17.0 312 1.0 7.97 3.4 15.0 310 0.9 7.72 4.16 17.0 312 0.6 8.55 4.27 17.0 310	L1 L2 H X 2	non-overlapping 1.3 10.05 3.46 18.0 258 1.7 11.13 3.87 17.0 261 1.0 9.45 3.81 18.0 267 0.6 10.88 4.11 19.0 260
	EMD 0.5 6.45 3.41 17.0 304	EMD 1.2 9.34 3.49 16.0 262
	half-overlapping L1 -0.5 10.04 5.64 20.0 2135 L2 -0.4 10.52 4.68 20 2175 H -0.3 11.11 5.99 21.0 2278 X 2 -0.9 6.71 4.14 19.0 2000 EMD -0.1 5.53 3.3 14.0 1867	half-overlapping L1 -0.3 8.03 3.03 14.0 1103 L2 -0.2 8.44 3.12 15.0 1090 H -0.3 7.13 3.16 14.0 1078 X 2 -0.6 8.12 3.05 15.0 1064 EMD 0.4 8.35 3.57 17.0 1043

from the computational eort, active contour approaches as presented by [START_REF] Jung | Nonlocal active contours[END_REF] are of interest because they are probably more robust to similar textured crosssections in the background.