Ultrasound (US) is the modality of choice for fetal screening, which includes the assessment of a variety of standardized growth measurements, like the abdominal circumference (AC). Screening guidelines define criteria on the scan plane, in which the measurement is taken. As US is increasingly becoming a 3D modality, approaches for automated determination of the optimal scan plane in a volumetric dataset would greatly improve the workflow. In this work, a novel framework for deep hyperplane learning is proposed and applied for view plane estimation in fetal US examinations. The approach is tightly integrated in the clinical workflow and consists of two main steps. First, the bounding box around the structure of interest is determined in the central slice (MPR). Second, offsets from the structure in the bounding box to the optimal view plane are estimated. By linear regression through the estimated offsets, the view plane coordinates can then be determined. The presented approach is successfully applied on clinical screening data for AC plane estimation and a high accuracy is obtained, outperforming or comparable to recent publications on the same application.