## 1 Introduction  
Breast cancer is one of the most common cancers, representing 25% of all new cancers and leading to 13% of all cancer-related deaths in Canadian women [1]. It has been well established that early detection of this disease before treatment is of the utmost importance, as five-year survival rates decrease significantly over time from \(\sim\)100% in stage 1 down to 22% in stage 4 because of the spreading of the disease to other vital organs [1]. Some of the most common diagnostic and screening procedures include manual examination, X-ray mammography, and breast magnetic resonance imaging (MRI). Unfortunately, some of these methods are too costly or insufficiently effective in detecting abnormalities or differentiating malignant tumors from benign lesions without follow-up biopsy. Taking advantage of the fact that malignant tumors tend to be stiffer than normal tissue and benign lesions, ultrasound elastography (USE) techniques have been developed as a cost-effective imaging technique to visualize tissue stiffness. While cost-effective, this technique can be used for preliminary assessment of malignancy [2; 3; 4; 5], hence potentially minimizing the number of follow-up biopsies. Typically, USE is performed through tissue mechanical stimulation, measuring the generated displacement field, and finally using this field to compute the tissue stiffness image. The quality of the stiffness image is highly dependent on the accuracy of the measured displacement field. Many methods have been developed for tissue motion tracking where tissue displacements are estimated by processing US radio-frequency (RF) data of the tissue as acquired at two states of before and after mechanical stimulation [6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. In this case, the mechanical stimulation is applied manually with the ultrasound probe, also known as quasi-static elastography. The comparative study presented here aims at assessing the qualifications of each major tissue motion tracking technique. Unlike other comparative studies where the qualifications are assessed based on signal-to-noise ratio (SNR) and CNR of the estimated displacement and strain fields, this study uses measures pertaining to [PERSON]'s modulus images reconstructed using respective tissue motion tracking methods for the assessment. One of the most significant issues plaguing quasi-static USE is the lack of high-quality data due to out-of-plane tissue motion, imperfect application of force, and other operator inconsistencies. PCA-GLUE was recently proposed for data quality assessment [18]. This is a machine-learning-based method developed using data pertaining to tissue mimicking phantoms and only 3 patients; thus, it may not be rigorous for clinical applications. Another potential avenue to address the data imperfection issue is to develop image processing techniques that are resistant to this imperfection. Such development, however, may involve unjustifiably extensive computational processing. One exception to this is the strain refinement algorithm (STREAL), which follows tissue-mechanics-based regularization to improve the estimate of tissue lateral displacements with very high performance and low computational cost [19; 20]. This method requires a rough initial estimate of the displacement field that can be obtained using previously developed techniques [7; 13; 21; 22]. This investigation aims at identifying the best rough displacement estimator method that can be used in conjunction with STREAL. The criterion for selection is the ability to provide a good balance of run-time and quality during the elastic modulus reconstruction. This is contrary to the commonly used criteria for displacement and strain image quality measured by their SNR and CNR. The candidate algorithms of initial displacement estimation include analytic minimization in 2D (AM2D) [7], Global Ultrasound Elastography (GLUE) [13], OVERWIND [21], and SOUL [22].