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The purpose of this paper is to explore a novel breast volume measuring method by mesh projection based on three-dimensional (3D) point cloud data.

Mesh projection method, a rapid and accurate method to calculate the volume of models described by triangular meshes, was transplanted to calculate breast volume based on 3D point cloud data derived from a [TC]2 3D scanner. A simple landmarking procedure was developed to decide breast boundary. Breast volumes derived from mesh projection method were compared to the results of water displacement by statistical analysis to validate its accuracy.

A novel breast volume measurement method is developed based on mesh projection method. By comparison of water displacement, mesh projection method is proved to be accurate to calculate breast volume. Furthermore, a simple and standard breast boundary landmarking procedure is established, which avoids the arbitrariness of the definition of breast boundary and improves the repetition of landmarking.

A simple and convenient tool is provided for bra industries to rapidly and accurately measure breast volume.

Mesh projection method is primarily applied to determine breast volume based on 3D point cloud data. Meanwhile, a simple and standard breast boundary landmarking procedure is put forward.

The purpose of this paper is to measure the breast volume of a large sample of women and their corresponding correctly fitted bra size, in order to demonstrate the range of volumes within each size and the variation amongst different bra sizes.

Breast volume of 104 women was measured via water displacement and was compared to their professionally fitted bra size, in the one style and brand of bra.

The mean breast volume of the left and right breast was 642 and 643 ml, ranging from 125 (size 10A) to 1,900 ml (size 24DD). The average professionally fitted bra band size was 12 (range size 10‐24; Australian sizing) and cup size was DD (range A‐G). A range of breast volumes was found to correspond to the same bra size and the volume of any one cup size was not homogenous amongst different band sizes.

Appreciating the range of breast volumes that correspond to each bra size is important in terms of both bra structure and design in order to provide adequate breast support. The large variation in cup volumes associated with different band sizes suggests women should not consider themselves to be an isolated cup size, but rather a combination of a band and cup size.

This is the first study to publish normative breast volume data, and the corresponding correctly fitted bra sizes, for a large sample of women. This is important information for bra design and to assist women achieve correct bra fit and support.

1.1. Logical Necessity of the Three Dimensions as a Unit of Thought The mathematician does not look kindly on the simple question of why natural space should consist of precisely three dimensions. Instead of giving an answer he assumes a silent smile and shows us a version of space with an infinity of dimensions, as if space were some kind of toy for him to fiddle with to his heart's content.

This paper aims to present an automated system that measures the volume of excavated soil in earthmoving operations. It focuses primarily on presenting the use of the radio frequency identification – real time location technology and image analysis techniques in isolation of stockpiles from their noisy backgrounds, extraction of their geometrical attributes and determination of their location.

An extensive literature review of image analysis techniques is performed to identify the ones most applicable in developing the proposed automated system. A set of techniques are selected and experimented to evaluate their effectiveness in the proposed application. A review of the state‐of‐the‐art distance measurement technologies is also conducted to identify the most suitable system to be used in the proposed system.

A set of image analysis techniques that positively contribute to the accuracy of the proposed system is identified. Geometrical attributes of stockpiles are automatically extracted for volume measurement purposes. The use of an affordable and reliable automated distance measurement tool is also suggested.

Although the proposed methodology is believed to be applicable to most configurations of stockpiles, it was tested on conical ones only.

The current practice of measuring the volume of excavated soil is time consuming and costly. Furthermore, it does not facilitate monitoring of excavation activities on close time intervals. The proposed system overcomes the problems associated with the current practice and provides an automated strategy that can be easily used by field personnel and/or home office management staff to closely monitor the progress of their earthmoving operations without physical human intervention.

The paper aims to highlight the importance of having an optical method that can accurately measure the surface finish of 3D printed parts and the influence this has on the total volume of the build.

The paper describes the application of digital moiré to the determination of the surface finish of 3D printed parts.

This study shows that surface roughness plays an important role in the volumetric analysis. There was an increase of 7 per cent from the total volume of the original CAD drawing; in total, there was 19 per cent more material deposited.

This methodology provides a robust tool for future research in the area of geometrical verification and optimization in addition to the potential use for residual stress determination.

This study shows that process optimization can be carried out more efficiently, and it is possible to determine the efficiency of an AM process by directly correlating the processing parameters and accurately comparing the prescribed CAD dimensions/volume to that of the as built part.

By reducing the amount of waste through process optimization, this leads to a reduced consumption of energy which can have a major impact on the environment.

This paper fulfills the need for high accuracy volumetric measurement of 3D printed components.

Describes a three‐dimensional machine vision technology for inspecting and measuring on‐line production. States that the 4DI three‐dimensional imager, a new machine vision technology developed by Intelligent Automation Systems, combines speed and accuracy to perform 100 per cent on‐line inspection and measurement of volumes and surfaces in real‐time. Until recently, neither conventional measurement techniques such as co‐ordinate measurement machines nor non‐contact optical technologies could inspect 100 per cent of production on‐line three‐dimensionally, being either too slow or too sensitive to ambient light. The 4DI uses structured laser light, multiple cameras and triangulation to capture moving or stationary objects. States this technology allows objects of different sizes, ranging from several feet to fractions of an inch to be imaged. States the system has no moving parts, it is robust in industrial environments.