This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

Segmentation in ultrasound (US) images is a challenge in computer vision, due to the high signal noise, artifacts that produce discontinuities in the boundaries and shadows that hide part of the received signal. In this paper, a solution based on ellipse fitting motivated by natural artery geometry will be proposed. To optimize the parameters that define such an ellipse, a strategy based on an evolutionary algorithm was adopted. The paper will also demonstrate that the method can be solved in a reasonable amount of time, making intensive GPGPU (general graphics processing unit, GPU, processing) where excellent computing performance gain is obtained (up to 54 times faster than the parallel CPU implementation). The proposed approach is compared with other artery segmentation methods in US images, obtaining very promising results. Furthermore, the proposed approach is parameter free and does not require any initialization estimation close to the final solution.

In medical imaging, one of the most important topics, which usually turns into a complex task, is image segmentation. Diagnosis based on the measurement of the dimensions of the artery allows experts to identify diseases, such as aneurysm. This disease produces an oversizing in the artery with the risk of a possible rupture. Hence, a good segmentation of the artery based on ultrasound (US) imaging is important, as it is used for diagnosing different vascular pathologies, such as aneurysm. US imaging represents a crucial medical tool to measure any oversize of the artery given its noninvasive nature, instead of other invasive techniques that make the use of contrast agents. These other techniques are inefficient and expensive as regards their actual cost, in terms of time consumption, and regarding the need for human resources with specific skills. Though US-based explorations require highly specialized personnel, approaches, such as the one described here, aim to create a valid tool, even for not so highly specialized staff.

This paper is focused on segmenting the outer side of the artery in US imaging, in an easy way, reducing the requirement for specific training, also reducing in this way the inter-intra-specialist variability and, thus, increasing the reliability of the measurements of the diameter of the artery. Semiautomatic measurement schemes, such as the one described in this work, also aim to facilitate the US exploration process, making it suitable even for medical personnel with less specific exploration skills.

Typical manually-driven measurement in ultrasound (US) software (TeleMed) to determinate the diameter of the artery.

The main contribution of this work is the proposal of a novel method based on the geometric nature of the artery, which adopts elliptical shapes. This method is able to segment the artery more accurately than other models proposed in the literature. The optimization of the seed ellipse parameters is done with an evolutionary optimization approach. Due to the high computational cost of the evolutionary models, it will make use of massive parallel architectures and present-day complex algorithms to carry out the segmentation in a reasonable time. The proposed approach is evaluated and compared with other well-known segmentation techniques, obtaining very promising results in comparison with the state-of-the-art.

Nowadays, many solutions have been proposed in natural imaging to detect ellipses. One of them is the approach proposed by Yao

The paper is organized as follows:

In this subsection, the most common segmentation methods in medicine will be briefly described and compared with the submitted approach.

Kass _{int}(v(s)) is the internal force, F_{ext}(v(s)) the external force, F_{const}(v(s)) another external force (e.g., one given by the user) and F_{Balloon}(v(s)) an external force that provides expansion or contraction to the contour. The internal force can be defined as in Equation (2).
_{cont}_{curv}, minimizes the curve, and

The original approach [_{ext}_{x} and _{y}

Zhang _{0} is the original image and

The Chan–Vese method has no problem with the leaks; for that reason, ∇g(|∇I|)^{T}·∇ϕ is removed, because it is no longer needed. Furthermore, the diffusion term in the original Equation (6) was substituted by a Gaussian convolution. Hence, the final equation after the modifications explained above is simplified as indicated in Equation (7).

Fuzzy C-mean (FCM) [

Incorporating shape prior knowledge has been one of the most recent advances in segmentation in the last decade. Cootes

The objective of this method is to estimate the parameters to locate the desired object to be segmented by means of matching each landmark with the previously trained normalized gradient profiles and solving linear equations to estimate the desired parameters in a multi-scale strategy. Those parameters are the translation in the _{x}_{y}

As an alternative to the described methods to segment the artery based on US images, this work is based on the proposal of a well-known stochastic technique. Storn and Price [_{c}_{c}_{c }_{c}_{c}_{c}

The pseudo-code of DE is shown in

Illustration fitted in the boundaries of an artery.

At this point, the main parameter optimization method used in this paper has been defined. The next subsection will detail the features extracted in the US image used by the DE model to find the desired ellipse parameters that define the best contour of the artery. This search will be led by an

To address the DE method over the solution space and estimate the parameters that obtain the best ellipse fitting over the artery, it is necessary to extract features that make it easier to find the desired solution. At first, the proposed approach must estimate the potential _{c}_{c}_{+ve}

To determinate the saliency map,_{n}_{n}^{(α)}_{n}

As opposed in the original version of this method, the normalization of Equations (13) and (14) and the integration of

At this point, one of the functions that will drive the DE method to optimize parameters _{c}_{c}_{x}_{y}_{xy}_{σ}

(

One of the main problems of working with US images is the amount of speckle noise. Yongjian and Acton [

Such noise will interfere in the pixel orientation estimation, as shown in

(

(

However, this information is not enough yet to address the search. Given the large solution space provided by the pixel orientation, edge information will be incorporated to define the echogenicity. A change of different tissue structures, such as muscle to fat or artery layers to blood, provides a high degree of echogenicity. For this reason, the Logarithmic Image Processing (LIP) edge detector [

Once the features that will drive the evolutive method to obtain the parameters (_{c}_{c}_{o}_{𝑔}_{b}_{FRS}_{c}_{c}_{c}_{c}

The first objective function Equation (21) is the orientation error, _{o}_{v}_{𝑔}_{v}_{b}_{v}_{FRS}_{1},_{2},_{3},_{4}, are incorporated for each respective objective function. After empirical tests, it was found that those values fixed to _{1} = 100, _{2} = 2, _{3} = 100, _{4} = 30 of the proposed method achieve satisfactory results.

One of the main problems when making use of evolutive schemes is the computation cost, because it requires many iterations (generations) and a considerable number of individual members in each population. To avoid this limitation, a well-known parallel computing architecture, GPU (graphics processing unit), is utilized. The GPU used to evaluate the proposed implementation is NVidia GTX 580 (Fermi architecture; NVidia Corporation, Santa Clara, Calif., US), and it is equipped with 512 processing cores. In this section, the same implementation is also compared with an Intel i7 CPU 950 (Intel Corporation, Santa Clara, Calif., US) that incorporates eight cores (four cores with two logic-cores per each physical one). The technology used to develop the methods, in both architectures, is Open Computing Language (OpenCL), motivated by its degree of versatility to be executed in different platforms. At this point, the implementation will be briefly described and the differences with other proposed methods in literature will be listed.

The differential evolution method has a 100% parallel nature and is very suitable for parallel architectures, such as GPUs [

Time consumption of the differential evolution algorithm in a (

The factor obtained on the GPU with respect to the parallel CPU implementation.

Once DE is evaluated in terms of computational speed on a GPU and parallel CPU, the feature extraction implementation in the US images (256 × 256) on the GPU is detailed. The parallel implementation of the SRAD and FRS methods will be explained in more detail, but the rest of the methods will not be described here, because their implementation is trivial and does not represent any kind of novelty. Nevertheless, all the performance rates of the specific modules are benchmarked in

SRAD, as well as non-lineal diffusion methods in general, is very expensive in computation terms. Weickert [

Computation time evaluation of the main methods used in the proposed algorithm on the graphics processing unit (GPU) and parallel CPU implementation. AOS, additive operator splitting; FRS, fast radial symmetry.

Method | GPU Time | CPU (8 cores) Time |
---|---|---|

SRAD (AOS)5 Iterations | 7.65 ms | 13.58 ms |

FRS | 3.78 ms | - |

Pixel Orientation | 1.14 ms | 6.95 ms |

Non-Max Suppression | 0.16 ms | 2.29 ms |

LIP-Sobel Gradient | 0.11 ms | 1.42 ms |

On the other hand, the FRS algorithm presents a sequential processing that becomes quite difficult to parallelize on a GPU. To solve this problem, Glavtchev

Finally, to conclude this section, the global time consumption is estimated. Choosing a population of 4,096 agents and 200 generations in the evolutionary scheme and the image processing analysis (detailed in

In this evaluation, the US images were acquired from two different US devices with the objective of evaluating the methods in a non-constrained platform. Those devices are a Siemens Antares (128 lines; Siemens AG, Munich, Germany) and a TeleMed Echo Blaster (64 lines; Telemed UAB, Vilnius, Lithuania). One of the most significant differences between these pieces of US equipment is their resolution (double resolution in Siemens with respect to the TeleMed device). To determine the accuracy of the methods, the well-known F-measure estimator Equations (26)–(28) are used. This estimator evaluates a benchmark dataset of 40 US images of different patients and areas, with their respective ground truth (where an expert marked it manually, point by point).

The stochastic method differential evolution was described in

DE/Best/1

DE/Current to Best/1

DE/Current to Best/2

DE/Rand/1

The evaluation of the proposed method with different mutation schemes with respect to the ground truth (manually marked) with its respective standard deviations (after 10 trials in each set up).

It is clearly demonstrated (

Evaluation of the proposed method with different features mixed (

The final comparative results of the F-measure, recall and precision with respect to other state-of-the-art methods. ASM, active shape model.

Finally, a last evaluation is carried out, where the results of the alternative methods (Section 2.1) and the proposed approach (

To obtain a more detailed evaluation between the proposed method and the second best in the ranking, both methods are compared by means of a Bland–Altman plot.

The Bland–Altman figure comparing the best two obtained results (the proposed one and ASM).

After the evaluation performed in the previous section, some results obtained with the assessed segmentation methods are exhibited, and the pros and cons of each model are discussed.

(

Comparing the group of methods that preserve the shape, it is important to remark that the parametric snake model provides different results in relation with its parameter settings (thus, it is sensitive to its internal configuration parameters). Another inconvenience occurs in the initialization of the method, which must be done close to the final solution. Those problems vanish with the ASM method, where the variation of the shape is defined in the training stage (avoiding parameter sensitivity), and its space search is longer than parametric snake, through its multiscale scheme. The suggested method does not require the training stage (unlike ASM), because it is based on the geometric nature of the artery, the ellipse.

As demonstrated in

Some results obtained with the proposed method in different patients.

In this work, a method based on an evolutionary approach for optimizing different kinds of features to fit an ellipse that best defines the edges of the artery has been proposed. It has been demonstrated that it can be computed efficiently making intensive use of a GPU platform. Its high accuracy in relation with other state-of-the-art methods is also highlighted.

The submitted approach outperforms other methods, not only in terms of accuracy, but also because in comparison with the ASM method, the suggested method does not require any kind of previous training stage. Another advantage that must be remarked upon is that the proposed method supports large search spaces, unlike ASM or parametric snakes, which need to be initialized close to the final solution.

In future research, we will extrapolate this approach to generalize the type of object to be segmented and will not be limited to geometric shapes.

This work has been supported by the Spanish Grant (AP2007-00275), the projects, ARC-VISION (TEC2010-15396) and ITREBA (TIC-5060), and the EU project, TOMSY (FP7-270436).

The work presented in this paper is a collaborative development by all the authors. Eduardo Ros and Rafael Ros defined the research line. Pablo Guzman designed and implemented the evaluated methods and performed the experiments.

The authors declare no conflict of interest.