Computational and Mathematical Methods in Medicine

Volume 2015, Article ID 343217, 8 pages

http://dx.doi.org/10.1155/2015/343217

## Motion Estimation Using the Firefly Algorithm in Ultrasonic Image Sequence of Soft Tissue

Department of Computer Science and Information Engineering, National Pingtung University, No. 4-18, Minsheng Road, Pingtung 90003, Taiwan

Received 4 October 2014; Accepted 29 January 2015

Academic Editor: Chuangyin Dang

Copyright © 2015 Chih-Feng Chao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Ultrasonic image sequence of the soft tissue is widely used in disease diagnosis; however, the speckle noises usually influenced the image quality. These images usually have a low signal-to-noise ratio presentation. The phenomenon gives rise to traditional motion estimation algorithms that are not suitable to measure the motion vectors. In this paper, a new motion estimation algorithm is developed for assessing the velocity field of soft tissue in a sequence of ultrasonic B-mode images. The proposed iterative firefly algorithm (IFA) searches for few candidate points to obtain the optimal motion vector, and then compares it to the traditional iterative full search algorithm (IFSA) via a series of experiments of *in vivo* ultrasonic image sequences. The experimental results show that the IFA can assess the vector with better efficiency and almost equal estimation quality compared to the traditional IFSA method.

#### 1. Introduction

The motion estimation not only is an important component of the block-based video compression but also is often applied in disease diagnosis for the image sequences of the ultrasound or the magnetic resonance images. The ultrasonic examination is widely used to present the soft tissues such as heart or muscle; however it is usually influenced by speckle noises and the temporal decorrelation of the speckle patterns [1]. The popular optical flow algorithm [2] is based on the assumption that the intensity of material point of the tissue in a complete image sequence is always invariant. This assumption is generally called intensity invariant constraint; however, there exist the speckle noises and the tissue deformations usually destroy the intensity constraints and therefore cause the difficulty of motion estimation.

Another approach for motion estimation problem is the block-matching algorithm [3–5]; it measures the motion vector by evaluating the similarity criterion, such as the mean square error (MSE), mean absolute error (MAE), and sum of absolute differences (SAD) between the corresponding blocks of two consecutive images. The block-matching algorithm is to find a candidate block within a search region of the corresponding image that best matches the current block in the current image. The displacement between these two matching blocks is called a motion vector (MV). The full search algorithm (FSA) [6, 7] is the simplest block-matching algorithm that can search in burst-force for the optimal estimation solution with minimal matching error as it checks all candidate search points at a time. However, it is extremely computational expensive at the searching process, and, therefore, its usage is seriously limited in the medical image sequences. The effective reduction of the number of search points can accelerate the motion estimation, which is based on the assumption that block distortion is monotonically decreasing. These algorithms are proposed to alleviate the high computational complexity of full search, including the three- or four-step search [8, 9] and the gradient descent search [10]. However, the ultrasonic images are usually noisy and with low signal-to-noise ratio due to the speckle noises and the decorrelation of the speckle patterns; as a result the monotonically decreasing assumption does not hold such that the usage of these algorithms always traps into local optima. In order to tackle this problem, the traditional motion estimation algorithms are revised into an iterative algorithm together with a specific smoothness constraint; however, these changes need a great amount of computation to estimate optimal motion vectors when we use the iterative full search algorithm (IFSA).

Recently, the algorithms of bioinspired computing (BIO) such as the honey bee mating algorithm [11] and shuffled frog-leaping algorithm [12] have been used to efficiently search for the global optimum in the complex optimization problems. Up to the present, there are few of BIO methods that addressed the problems of motion estimation in the ultrasonic image sequence. Among them, the firefly algorithm is another algorithm that had been used in the image thresholding and vector quantitation [13, 14]. In this paper, we present an iterative algorithm that builds in the firefly algorithm for motion estimation. The proposed algorithm is introduced in Section 2. In Section 3, we demonstrate the experimental results. The conclusion and final remarks are given in Section 4.

#### 2. Material and Methods

The problem of estimating motion field from image sequence has been studied extensively. The block-matching algorithm is the most popular because of its simplicity. Section 2.1 will briefly describe the block-matching algorithm. Section 2.2 introduces the firefly algorithm. In order to handle the problem of speckle noises, we designed an iterative firefly algorithm (IFA) together with a smooth constraint to estimate the motor vectors, described in Section 2.3.

##### 2.1. The Block-Matching Algorithm

Because of its simplicity, the block-matching is a widely used algorithm in motion estimation. In matching procedures, the estimated image block of the processing frame will correspond to the best matching location within the predefined search window of the reference frame, as shown in Figure 1. In general, the size of estimated block, ispixels and the size of the corresponding search window is . These two windows are centered at the same pointin the two consecutive image frames (and). The full search searches for all possible locations within the search window by evaluating some matching criteria and selected one locationof the corresponding block. The relative displacement of the two locations of bothand is defined as the motion vector,,, .