Abstract—This paper is focused on localization of objects in

medical images. A novel improvement of an existing method for localization of artery in longitudinal ultrasound B-mode scan is proposed in the paper. The localization is based on a classification of pixels according to image information in their neighborhood. To suppress misclassified points, a novel RANSAC based method is proposed. This method is able to find the most appropriate mathematical model of depicted common carotid artery (CCA) on the basis of previous classification. The proposed RANSAC based method with its mathematical footing is described in detail and the results of method within the algorithm for localization of artery are enclosed. By using the proposed RANSAC based method the localization method becomes very robust.

Keywords—ultrasound image, localization, artery, RANSAC model, classification.

I. INTRODUCTION he method for artery localization is very important, because it is the basic step in the systems for automatic measurement of arterial parameters such as lumen

diameter (LD), artery stiffness (AS), or intima media thickness (IMT). The results of such measurements can be directly used for the prediction of patient’s risk of cardio-vascular events (CVE) [1]. Nowadays, there are not many automatic systems for the measurement of arterial parameters, especially due to low-examined issue of localization of artery. Localization procedure is very important for such systems because it ensures the reliability of automated systems.

The article presents a significant improvement of the procedure for localization of artery (see Fig. 1) introduced in [2]. The proposed improvement considerably increases the robustness of the localization procedure. The main improvement resides in the modification of a part of the algorithm that originally uses the classical RANSAC [3] method. This classical RANSAC method has been completely replaced by a novel RANSAC based method which uses a nonlinear model of artery. Due to such adjustment of the localization procedures, all limitations of comparable methods are completely eliminated, including the impossibility of precise localization of a curved artery and non-horizontally captured artery.

Most of the automated methods for artery localization are

Manuscript received May 04, 2011. This work was prepared with the

support of the MSMT project No. 2B06111, ME10123, and FRVS 2502. R. Benes is with the Faculty of Electrical Engineering and

Communication, Brno University of Technology, Udolni 244/53, CZ-60200 Brno, Czech Republic (e-mail: radek.benes@phd.feec.vutbr.cz).

M. Hasmanda is with the Faculty of Electrical Engineering and Communication, Brno University of Technology, Udolni 244/53, CZ-60200 Brno, Czech Republic (e-mail: xhasma01@stud.feec.vutbr.cz).

K. Riha is with the Faculty of Electrical Engineering and Communication, Brno University of Technology, Udolni 244/53, CZ-60200 Brno, Czech Republic (e-mail: rihak@feec.vutbr.cz).

not robust and often unable to deal with fundamental problems that occur during capturing the artery. Due to the disadvantages of existing localization methods mentioned above, the proposed method has been designed for the highest robustness as possible. The novelty of the localization method resides in the design and implementation of a RANSAC based method for fitting a data using nonlinear model of artery. In the paper, this novel method is described in detail.

The paper is organized as follows. Related work is presented first, then, in the third section, the proposed method for artery localization is briefly described. Fourth section describes the novel RANSAC based method, which improves the localization method presented in the third section. Results are summarized in section five and the last section concludes the paper and suggests possible directions of future research.

II. RELATED WORK Nowadays, the process of localization of artery can be

manual, semi-automatic or automatic. If the localization is manual, some inaccuracies can occur during further processing of images (segmentation, measurement). This inaccuracy is caused due to slightly different localization made by different operators (doctors). Manual localization is used for example in [4], where operator must select two points on the arterial wall. In [5] operator has to select even more than two points on the arterial wall.

In many approaches the localization procedure is semi-automatic. For example the operator (doctor) selects the region of interest (ROI) that encloses searched artery [6]. Such additional information dramatically simplifies the localization procedure, because most problematic areas in an ultrasound (US) image (other tissues that are similar to the CCA) may not be taken into account.

To our knowledge, there are only a few automated methods for artery localization, but they are very simple, and thus not so robust. For example Fan et al. [7] design the localization method that analyzes the intensity and the standard deviation of pixels and their small neighborhood. Described method can fail if the captured artery is slightly curved. Also the Hough transformation [8] in the localization procedure has been examined, but linear model used in such approaches is unable to localize curved arteries.

Conversely to above mentioned methods, our method is fully automated (need no interaction with operator) and robust against possible problems during the capturing of artery. The method is also absolutely independent on the rotation of the artery in the image and is capable of localization of curved arteries.

III. ARTERY LOCALIZATION The block diagram of the proposed method for CCA

localization in longitudinal scan is depicted in Fig. 1. This

Object Localization in Medical Images Radek Benes, Martin Hasmanda, and Kamil Riha

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978-1-4577-1411-5/11/$26.00 ©2011 IEEE TSP 2011559

method starts by sampling of input image and by extraction of image features. The samples from input image are subsequently classified. The SVM classifier [2], [9] classifies the points into one of two categories: “artery points” and “other points”. In further processing, only points classified as “artery points” are considered (see Fig. 6). In the set of points classified as “artery points” prevail such points that were correctly classified as “artery points”, but there are also some points that are not artery pixels (due to misclassification by SVM – see Fig. 9). Thus the proposed RANSAC based method is used to estimate parameters of a mathematical model of artery from a set of points which contains outliers (misclassified points).

A. Input data set of images The set of 57 B-mode ultrasound images, captured by

Sonix OP, have been used for this experiment. All images are depicting CCA in longitudinal scan (see Fig. 5) of different volunteers. The images were scanned with different settings of acquisition hardware (frequency, depth, gain) and different positioning of a probe. For each input image, an appropriate mask has been created to define the artery position in input image (see Fig. 8). These images and masks have been used for training and validation purposes and therefore the set of images were divided into two disjunctive groups – training and testing set. The training data set has been used for the training of the SVM classifier and the testing set has been used for the performance evaluation of the proposed method.

B. SVM classifier The classification was performed on the basis of image

local features obtained from a neighborhood of particular pixels. The appropriate selection of features is crucial for the performance of the classifier. It is important to select features that separate both classes. In this implementation, appropriate features were selected according to our experience – the mean value in the neighborhood, standard deviation, median value, center of the mass, maximal intensity, minimal intensity, and others.

IV. PROPOSED RANSAC BASED METHOD Generally, RANSAC [3] is an iterative algorithm that is

able to estimate parameters of a mathematical model from a

set of points which contains outliers. Outliers are points that are numerically distant from the rest of the data. RANSAC is not a deterministic algorithm, thus the results are produced correctly only with a certain probability.

Proposed RANSAC based method, which is a part of the localization procedure (see the block diagram of localization procedure in Fig. 1), processes all points classified as “artery points”. There are certain misclassified points (see Fig. 9) among these points. In RANSAC terminology these misclassified points are called outliers. The proposed modification of RANSAC algorithm is capable to find the most suitable non-linear mathematical model that approximates the artery and thus decide which points are outliers and which are inliers.

The utilization of RANSAC algorithm is enabled due to appropriate geometrical configuration of inliers in an input image and due to small number of outliers. The outliers are only isolated points or they form small clusters, but they never form a compact cluster comparable with a cluster formed by inliers.

Classical RANSAC algorithm utilizes only a linear model that is not appropriate for curved arteries (see Fig. 5). Therefore, a nonlinear mathematical model is implemented in the proposed RANSAC based method. Nonlinear mathematical model is in our implementation represented by an explicit polynomial curve (second order). The second order of polynomial curve is sufficient, because arteries are not extensively curved. The second order polynomial curve can be expressed by the equation . (1)

RANSAC algorithm iteratively selects a random subset of input points and estimates the parameters of mathematical model. Estimated model is evaluated by the test against the input data and the subsequent computation of inliers. The algorithm is summarized in Algorithm 1 and a mathematical footing for it’s the most important steps will be described in following subsections.

A. Construction of polynomial curve through three points Second order polynomial curve used in the RANSAC

based method can be defined by the Eq. (1) or in matrix form

Fig. 1. Block diagram of proposed localization method.

Algorithm 1. The proposed RANSAC based method 1. Repeat steps a) – c) for selected number of iterations

a) Select three points (hypothetical inliers) and construct the polynomial curve through these three points (described in section A).

b) Test all other points against the model a. Compute the distances x from this curve for all points x (according to section B). b. Points that satisfy the criterion are inliers ( threshold).

c) If the actual number of inliers is greater than the temporary highest number of inliers, than the model and the temporary number of inliers is saved.

2. Interpolate line through all inliers in saved model (described in section C).

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Fig. 2. Construction of polynomial curve through three points.

Fig. 3. Computation of the distance between point and a polynomial curve.

1 . (2)

Three points , , 0,1,2 are enough for fitting the quadratic polynomial curve (see Fig. 2). It can be written in matrix form 111 . (3)

The solution of this system is a vector of parameters of the fitted polynomial curve T. B. Computation of the distance between point and a polynomial curve

The distance between an arbitrary point and the polynomial curve is defined as a distance between point and the nearest point on curve (as can be seen in Fig. 3).

Generally, the Euclidian distance between two points , and , is defined as . (4)

Points on the curve defined by Eq. (1) have coordinates , , . The distance between points on the curve and an arbitrary point , , can be expressed by the function of parameter . (5)

The point on the polynomial curve that is closest to have minimal distance and thus it can be found as a minimum of Eq. (5).

Fig. 4. Approximation of polynomial curve through more than three points.

0, (6)

4 6 2 1 22 0. (7)

The roots of the cubic function (Eq. (7)) can be computed by several methods (according to [10]). The real root defines the -coordinate of the nearest point on the curve. The

-coordinate of this point can be computed by using Eq. (1). The searched point , is the point on curve nearest to the point and the distance is (8)

C. Approximation of polynomial curve through more than three points The RANSAC algorithm finds the best mathematical

model of artery and appropriate inliers. The final step of the proposed algorithm is the re-computation of best model by considering all inliers. Therefore, the proposed method has to be able to fit (approximate) the polynomial curve through more than three points (see Fig. 4). The approximation is a process of searching of the best model that approximates all points with minimal approximation error. All approximated points must satisfy the equation of mathematical model with a minimal error. To solve such problem, an approximation error must be added to the mathematical model of polynomial curve . (9)

The set of equations (for approximated points) can be rewritten in a matrix form 11 . (10)

Because the number of points is greater than three ( 3) the system is overdetermined. The least squares method is a standard approach to approximate solution of overdetermined systems. The overall solution minimizes the sum of the squares of the errors of every single equation. In our implementation such system of equations is solved by singular value decomposition (SVD) [11].

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Fig. 5. Input image.

Fig. 6. Points classified as “artery points” deimage.

Fig. 7. Result of proposed RANSAC algorithm

D. Performance optimization of RANSAC The performance of proposed RANSAC

been improved by using the implementatioIn this modification the number of iterationand can be reduced within the algorithm acc

,

where the probability constant [3] is com0.99. The parameter is the number of

epicted into the original

m.

based method has on inspired by [3]. ns is not constant cording to

(11)

mmonly chosen as f randomly chosen

Fig. 8. Appropriate mask that d

Fig. 9. Points classified as “arimage with the description. Highl

points, in our mathematical mevaluates the probability, that th1 ,

where is the number of inliepoints.

V. RE

The validation data set contamasks. These images were capresearch team. The accuracy oand it guarantees the small amois advantageous for further procbased method.

For the evaluation of the lsuccess rate. The success ratelocalization and all localizatiowas considered as successful ifartery in whole image) betweemodel (green curve in Fig. 7) (estimated from mask in Fig. 8)artery width. The localization wthe validation data set, thus thecomparison with original improvement increases the succ

M

define the precise location of artery.

rtery points” depicted into the original ighted the misclassified points.

model 3. The parameter he selected point is outlier

(12)

ers and is the number of all

ESULTS ains 30 images with particular ptured at the workplace of the f SVM classifier was 91.22 %

ount of misclassified points that cessing by proposed RANSAC

localization process we use a e is a rate between successful on attempts. The localization f all distances (measured along en the center-line of searched and real center-line of artery

) do not exceeds 1/3 of average was successful in 29 images of e success rate was 96.67 %. In method [2], the proposed

cess rate by 3.3 %.

Misclassified points

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VI. CONCLUSION In this paper, a significant improvement of the method for

CCA localization in longitudinal ultrasound images has been described. The method is designed to completely eliminate drawbacks of comparable methods such as incorrect localization of non-horizontally displayed arteries and curved arteries. In the proposed implementation, the SVM classifier is used with the accuracy 91.22 % (measured on the independent validation set).

The proposed improved localization method was tested on validation set and the artery was correctly localized in 29 of 30 images (success rate 96.67 %). Proposed modification of localization method led to increase of the success rate by 3.3 %.

In the future, it is planned that the classification step of localization algorithm will be improved by using the most suitable features determined by a genetic algorithm. This technique can led to significant increase of the classification accuracy and subsequently increase the success rate of entire localization procedure.

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[4] D.-C. Cheng et al. “Using snakes to detect the intimal and adventitial layers of the common carotid artery wall in sonographic images.” Computer Methods and Programs in Biomedicine, vol. 1, pp. 27 – 37, 2002.

[5] H. N. Hodis et al. “The role of carotid arterial intima-media thickness in predicting clinical coronary events”. Annals of Internal Medicine, pp. 262 – 269, 1998.

[6] D. C. Cheng et al. “A novel method in detecting CCA lumen diameter and IMT in dynamic B-mode sonography”. In 13th International Conference on Biomedical Engineering, vol. 23, pp. 734 – 737. Berlin, 2009.

[7] L. Fan et al. “Ultrasound measurement of brachial flow-mediated vasodilator response.” IEEE Transactions on Medical Imaging, vol. 19, pp. 621 – 631, July 2000.

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[9] V. Vapnik, The Nature of Statistical Learning Theory, John Wiley, New York, USA 1995.

[10] Dickson, L. E. "A New Solution of the Cubic Equation." Amer. Math. Monthly 5, 38-39, 1898.

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