The thyroid is one of the largest endocrine glands in the human body, which is involved in several body mechanisms like controlling protein synthesis and the body's sensitivity to other hormones and use of energy sources. Hence, it is of prime importance to track the shape and size of thyroid over time in order to evaluate its state. Thyroid segmentation and volume computation are important tools that can be used for thyroid state tracking assessment. Most of the proposed approaches are not automatic and require long time to correctly segment the thyroid. In this work, we compare three different nonautomatic segmentation algorithms (i.e., active contours without edges, graph cut, and pixel-based classifier) in freehand three-dimensional ultrasound imaging in terms of accuracy, robustness, ease of use, level of human interaction required, and computation time. We figured out that these methods lack automation and machine intelligence and are not highly accurate. Hence, we implemented two machine learning approaches (i.e., random forest and convolutional neural network) to improve the accuracy of segmentation as well as provide automation. This comparative study intends to discuss and analyse the advantages and disadvantages of different algorithms. In the last step, the volume of the thyroid is computed using the segmentation results, and the performance analysis of all the algorithms is carried out by comparing the segmentation results with the ground truth.