# Trackerless 3D Freehand Ultrasound Reconstruction: A Review
## 1 Introduction  
Two-dimensional ultrasound (2D US) has established itself as an invaluable imaging modality in clinical settings due to its low cost, portability, and non-invasive nature. Its real-time visualization capability offers significant utility in intraoperative procedures, providing clinicians with essential anatomical and functional information. Despite these advantages, 2D US is hindered by limitations such as limited spatial orientation, lacking valuable 3D context, and its dependence on the operator's experience and interpretive skills. These constraints underscore the inherent variability and the potential for subjectivity in 2D US [1]. The introduction of three-dimensional ultrasound (3D US) marks a significant advancement, addressing many of these limitations. Specifically, 3D US provides a more comprehensive visualization of anatomical regions of interest (ROIs) and provides the flexibility of examining the acquired data from multiple viewpoints post-acquisition. This allows for more accurate quantitative measurements and additionally reduces the variability due to operators. Moreover, 3D US allows for integration with other 3D imaging modalities, such as MRI or CT. This enables a multifaceted view of the patient's anatomy, enriching the diagnostic process. With these advancements, 3D US extends the potential of2D US across a broader spectrum of clinical applications, like surgical planning, monitoring of treatment progression, and a wide range of intraoperative and interventional tasks [2]. The path to realizing 3D US reconstructions has seen various methodologies, including the use of 3D US transducers, external tracking, and image-based reconstruction methods. Such 3D US transducers employ 2D crystal arrays rather than traditional 1D crystal arrays. This design facilitates the electronic steering and focusing of the US beam in multiple dimensions, thereby enabling the real-time acquisition of 3D volumetric data. However, since the transducer elements are spread across two dimensions, this configuration results in fewer elements in each dimension. Therefore, to maintain a sufficient spatial resolution the imaging system must limit the coverage area, resulting in a smaller field of view (FOV), particularly at greater depths. External tracking devices such as mechanical, optical, or electromagnetic (EM) systems are designed to position the US probe in 3D space. These systems are prone to artifacts caused by magnetic interference or optical occlusion and have constraints in the range of motion. Considering the high costs and cumbersome set-up of 3D US transducers and external tracking systems, their suitability for certain clinical applications like intraoperative and point-of-care US (POCUS) is diminished [3; 4]. Image-based freehand 3D US represents a promising alternative, eliminating the need for both external tracking devices and 3D transducers, thereby capitalizing on the potential for integration with cost-effective, portable, and sometimes wireless, US devices [5]. The computational challenge of these systems lies in the reconstruction process, which necessitates an accurate estimation of the probe's trajectory, divisible into in-plane and out-of-plane (elevational) movements. While in-plane movements are more readily quantified, out-of-plane estimations remain complex. Prior research on out-of-plane motion dates back to seminal work by [PERSON] et al. [6] and has been mainly based on speckle noise, the granular gray-scale textures in B-mode US images. Speckle decorrelation methods map the transformation between neighboring US images to the correlation of their speckle patterns, i.e., the higher the speckle correlation, the lower the elevational distance between neighboring frames [7]. Under Rayleigh scattering conditions, where the size of these scatters is much smaller than the wavelength of the sound waves, this speckle pattern is theoretically predictable.