## 1 Introduction  
As pointed out in several studies [1; 2; 3; 4; 5; 6; 7; 8; 9], in recent years quality assurance (QA) programs, able to objectively provide ultrasound (US) parameter measurements, have become more and more important in the assessment of US scanner functionality, given that they are implied in a wide range of well-known clinical applications for the visualization of anatomical districts worldwide. It is therefore of primary importance to make sure that clinicians can identify and characterize possible abnormalities in an anatomic image (e.g., malignancies). This should be possible at any depth with the highest reliability, resulting in an improvement of both diagnostic and therapeutic phases and in a reduction of the clinician mismatching to the minimum as well as patient discomfort due to wrong therapeutic choices. Such results can be achieved as long as the US scanners are able to provide a consistent quality in the images after having checked several B-mode US parameters. Among the main ones, maximum depth of penetration (DOP) deserves particular attention--defined as the maximum low contrast penetration depth at which US speckle due to the scattering within a tissue-mimicking material (TMM), is displayed by the US scanner without noise [1; 2; 4; 8; 10; 11]. In particular, speckle pattern is prominently displayed in the image when considering depths much smaller than DOP, while the situation changes at greater depths than DOP where the electronic noise is predominant with respect to speckle. The DOP is an indicator of how well the US probe is able to display the features of anatomical districts far from the probe-skin/phantom interface. [PERSON] et al. suggested that it could be considered a predictor for the clinician's image quality perception [12]. Nowadays, there is neither a wide consensus nor a commonly-accepted method for DOP estimation and in many cases it is still visually assessed [13; 14]. However, it should be highlighted that DOP operator dependence is detrimental for assessment objectivity. On the other hand [PERSON] et al. [15], after having defined DOP as the depth where speckle starts to be dominated from noise, pointed out how its estimation is necessary because of its influence on vertical distance accuracy measurements. Another scientific study [16] provided an alternative definition of such parameters as the maximum depth at which speckle is still visible. The estimation was based on the standard deviation computation of both speckle and noise, from two consecutive images captured by holding the probe still. Nevertheless, image analysis-based off-line methods have been proposed in literature [10; 11; 17; 18; 19] aimed at overcoming the intrinsic limit of subjective visually-performed tests. Among the most used, the SNR-based evaluation at several depths deserves to be mentioned [20] since it is reported as a standard reference method in [17]. In particular, such methods involve the storage of images captured from a US phantom [7; 19; 21] and consequently DOP is evaluated in the post-processing phase as the maximum depth at which the estimated SNR exceeds a set threshold. Despite the development of such methods, it should be pointed out that the most accredited ones are based on a threshold value subjectively chosen by the operator [4] or without clarifying the choice criteria [16; 19]. This constitutes a source of error and unreliability because such methods suffer from an indirect operator subjectivity. The contribution of the present work lies firstly in the fact that the proposed method is no longer based on threshold values chosen by users or operators but it determines the thresholds in an a totally independent and automatic manner--this is a great advantage in terms of reproducibility and reliability of the results. Secondly, in order to validate this novel method, it was compared with another operator-independent algorithm, already proposed in literature by the same authors [18], whose complexity may make it harder to employ.