# Estimation of the Prostate Volume from Abdominal Ultrasound Images by Image-Patch Voting
## 1 Introduction  
Prostate volume is a crucial parameter in many clinical practices. It plays an essential role in the diagnosis of benign prostatic hyperplasia (BPH) [1]. BPH is a widespread prostatic disease that affects most aged men [2]. Clinicians use prostate volume while managing lower urinary tract symptoms (LUTS) [3]. Another critical area for prostate volume is the calculation of the Prostate-Specific Antigen Density (PSAD) value to detect and manage prostate cancer (PCa) [4]. PCa was the second most prevalent cancer for the year 2020 and the most prevalent cancer for the last five years among men [5]. PSAD plays a role as one of the criteria for active surveillance decisions in clinical practice [6]. Combining PSAD with other scores may help to decide biopsies [7]. There are many medical-imaging technologies to estimate prostate volume. Widely used technologies are Magnetic Resonance Imaging (MRI), Computed Tomography (CT), and Ultrasound (US) [8]. US technology differs from others with its portability, low-cost, and harmlessness, and it allows experts to scan the prostate in real-time [9]. Trans Rectal Ultrasound (TRUS) and Abdominal Ultrasound (AUS) technologies are frequently used in prostate applications. As shown in Figure 1, despite its better imaging quality with a higher Signal-to-Noise Ratio (SNR) and a larger view of the prostate with no other anatomic structures, TRUS technology is difficult to use regularly during successive radiotherapy sequences [10] due to patient discomfort [11]. The AUS technique is an easy-to-use alternative US imaging technology and is often used where TRUS is not practical. Conventionally, a prostate-volume measurement is done manually on medical images by experts. Manual volume estimation results in high intra-expert and inter-expert difference due to factors caused by imaging quality, personal experience, and human error [12],which suggests that the guidance of experts by automatic systems would be beneficial. Automated prostate-volume-estimation systems are also essential to reduce the time spent while measuring the prostate volume. Segmentation and contour extraction methods are used in many studies to infer the prostate volume. However, when AUS images are considered in problems such as low SNR, artifacts and incomplete contours challenge even the state-of-the-art deep-learning techniques. That makes AUS imaging a rarely studied method for automatic prostate-volume measurement systems. This study aimed to demonstrate that an AUS-based automated system for measuring the prostate volume can be an alternative to TRUS, MRI, or CT-based systems. In our study, we developed a method for estimating prostate volume by following the steps of the standard ellipsoid volume formula, which is not easily applicable in an end-to-end automated system. Our system gives both intermediate and final results, allowing both manual intervention and fully automated employment. To measure prostate volume, we estimated the three major diameters of the ellipsoid representing the prostate. Estimation of diameters was made by detecting four points from transverse and two points from sagittal AUS images. We call these points diameter endpoints. To overcome the characteristic problems of AUS images, we developed a voting-based method to detect points where various locations vote for distance and orientation values relative to each diameter endpoint. We designed a novel network model to carry out the voting process. We were unable to compare our volume-estimation results with other studies as almost no other studies are available to estimate prostate volume from AUS images. Instead, we evaluated the difference in intra- and inter-expert volume estimates on AUS images and compared these values with our system estimates. Due to the higher SNR values and better image quality compared (Figure 2) to both AUS and TRUS images (Figure 1), MR image annotations are considered the gold standard [13] in prostate applications.