Challenging Zero Error in Point Cloud Volume Calculation! Achieving High Precision with the Latest Technologies

Table of Contents

• Introduction

• What Is Volume Calculation Using Point Clouds

• Comparison with Traditional Methods: Advantages of Using Point Clouds

• Error Factors in Point Cloud Volume Calculation

• Challenging Zero Error: Latest Technologies Supporting High Precision

• Simple Surveying with LRTK

• FAQ

Introduction

In civil engineering and construction sites, volume calculations—such as embankment volumes and spoil quantities—are essential tasks for project planning and cost control. Measurement results serve as the basis for as-built management and progress quantity determination, so rapid and accurate volume calculations are required on site. Traditionally, these volume calculations required skilled surveyors to carefully measure cross sections in the field and then produce drawings and perform calculations in the office. However, with the recent promotion of ICT construction, digital surveying using 3D data and GNSS is rapidly spreading. As a result, volume calculations that used to require time and specialized skills are becoming something that virtually anyone can perform easily. This article focuses on volume calculation using "point cloud data," comparing it with traditional methods, explaining points for improving accuracy, and introducing the latest technologies that can bring us close to "zero error." Finally, we introduce an easy field-deployable method, "simple surveying with LRTK."

What Is Volume Calculation Using Point Clouds

Point cloud data are three-dimensional data that record the shape of objects in space as an enormous collection of points. Each point includes X, Y, and Z coordinates (position information including elevation), and the set of points reproduces the surface of objects or terrain in detail. For example, scanning terrain with a laser scanner (LiDAR) can obtain a high-density point cloud of millions of points in a single measurement. Photogrammetry can also generate point cloud models from images taken by drones or cameras. When the acquired point cloud data are imported into specialized point cloud viewer software or cloud services, they can be freely inspected in a 3D model space, and distances, areas, and volumes of arbitrary regions can be measured.

Volume calculation using point clouds is the method of calculating the volume of land or structures on these point cloud data. Specifically, you enclose an arbitrary region in the point cloud and automatically calculate the volume of embankment or accumulated material within that region. In the past, point cloud data had to be converted into a meshed surface model and the model’s volume calculated. But recently, features have appeared that allow direct volume calculation from point clouds with a single click in a point cloud viewer. In other words, even without advanced 3D CAD skills, as long as you can acquire point cloud data, you can quickly and accurately calculate volumes.

Comparison with Traditional Methods: Advantages of Using Point Clouds

Traditional volume calculations often depended on manual work by experienced surveying technicians. A typical example is measuring many terrain cross sections on site with a total station or level, then calculating volume using the average cross-section method from those cross sections. However, this method can fail to reflect fine irregularities between cross sections (such as depressions or bulges), leading to discrepancies from the actual volume. Increasing the number of measurement points per cross section can improve accuracy, but it also increases workload. The traditional process—carrying heavy equipment, surveying with multiple people, and then drawing and calculating after measurement—was very time-consuming. While a simple method using a handheld GPS to take points was an option, conventional GNSS-only positioning had errors of several meters and could not be used for volume calculations that required precision.

Using point cloud data, however, allows automatic acquisition of high-density measurement points in a short time, recording the site shape without omission. For example, a laser scanner can measure a wide area in minutes, and drone photogrammetry can model vast sites quickly. Even smartphone or tablet LiDAR can capture surrounding 3D point clouds in a few minutes simply by walking around the site. Because point clouds contain vastly more data than traditional surveys, they do not overlook features between cross sections and can calculate accurate volumes that reflect even small irregularities and slopes. As a result, compared to traditional methods that relied on extrapolation from limited points, quantity estimation becomes far more reliable. Point cloud measurement data are also objective records that yield the same results regardless of who performs the measurement. There is less room for human variation or subjectivity, making it easier to present substantiated figures to clients and stakeholders. Once acquired, point cloud data can be archived digitally, and any cross section can be cut later and recalculated at will. Additional volume calculations can be performed on the data as needed, preventing errors due to missed measurements. In this way, point cloud–based methods greatly outperform traditional methods in both efficiency and accuracy.

Error Factors in Point Cloud Volume Calculation

That said, using point cloud data does not automatically yield zero error. Various factors can introduce measurement and calculation errors even with point clouds. Here we organize the main error factors that affect point cloud volume calculation.

• Measurement instrument accuracy: The performance of the instruments used directly impacts accuracy. For laser scanners, the timing accuracy of the distance-measuring laser and the angular accuracy of the rotation mechanism influence positional errors of each point. Higher-performance instruments have better catalog specifications and may claim distance errors of ± a few mm under ideal conditions. However, field conditions seldom match ideal conditions, and performance can degrade due to light reflection, temperature, humidity, and other environmental factors. In photogrammetry, camera resolution and lens distortion correction accuracy also affect positional accuracy.

• Point cloud resolution and density: The point density and resolution of the point cloud also affect accuracy. If the spacing between acquired points is too coarse, small irregularities or boundaries may not be captured, resulting in under- or overestimation of volume. For example, the Ministry of Land, Infrastructure, Transport and Tourism’s guidelines require that when using a ground-based laser scanner for earthwork, measurement density should be at least 1 point per 0.01 m² (100 points per 1 m²). Higher-density point clouds reproduce shapes in more detail, but measurements from greater distances inevitably increase spacing between points and reduce effective resolution. You need to adjust instrument settings and measurement positions so that density is appropriate for the measurement range and angles.

• Registration error (alignment error): On large sites, point clouds are typically captured from multiple positions and merged to create the overall dataset. The registration error between point clouds cannot be ignored. Even when using target markers or known points, small misalignments can accumulate into distortions of several centimeters across the entire dataset. Mobile mapping and SLAM-based methods that measure while moving are particularly susceptible to cumulative self-positioning errors that cause point cloud distortions over distance. To prevent this, it is important to measure fixed reference points at key locations for joining, or to perform full-circuit measurements to cancel closing errors.

• Environmental conditions and properties of the target: Measurement environment also affects accuracy. In laser measurements, rain or fog scatters and attenuates the laser, causing noise and missing points. Under strong direct sunlight, smartphone-embedded infrared LiDAR may degrade in performance. In photogrammetry, backlight or low-light conditions make feature detection difficult and reduce accuracy. The material and color of target objects matter as well. Black objects tend to absorb light and may not appear in laser point clouds, mirrors and water surfaces can cause incorrect reflections and mismeasurements, and transparent glass can let the laser pass through, making point cloud acquisition difficult. In such cases, consider countermeasures like applying a matte sheet or spraying white coating on the object before measurement.

These factors can combine to introduce some error and variation into point cloud data. However, a major advantage of point clouds is the extremely large number of measurement points. Random errors of individual points tend to cancel out by averaging, so the overall shape can be captured with high accuracy. In other words, even if individual point errors are on the order of several centimeters, fitting a plane or surface to tens of thousands of points may allow surface shape estimation at millimeter-level accuracy. Therefore, minimizing error factors while leveraging the statistical accuracy improvement effect of large point cloud datasets is the key to high-precision volume calculation.

Challenging Zero Error: Latest Technologies Supporting High Precision

While achieving literally "zero error" is theoretically difficult, the latest technologies make it possible to reduce surveying errors to near zero. This chapter introduces the latest technologies that support high-precision point cloud volume calculation and the specific approaches used.

● High-precision instruments and multi-view measurements: On the hardware side, measurement instruments such as laser scanners are evolving and improving accuracy year by year. High-performance TLS (terrestrial laser scanners) can acquire millimeter-level point clouds, and the error of each of the millions of points captured at once is kept very small. Acquiring overlapping point clouds from multiple viewpoints and integrating them is also effective for reducing blind spots and canceling errors. For example, scanning the object from additional directions can complement shadowed areas not visible from one side, and averaging errors in overlapping regions increases the reliability of the shape. Recent studies also report improved object volume estimation accuracy when integrating point clouds from different viewpoints. Planning measurement viewpoints to capture the target from as many angles as possible is a fundamental principle for improving precision.

● Combining with GNSS (high-precision positioning): Combining point cloud measurement with high-precision GNSS positioning technologies (RTK or PPK) can dramatically increase the absolute accuracy of the entire point cloud. Historically, point clouds acquired by drones or laser scanners required post-processing alignment to known points or ICP algorithms. By using RTK-GNSS together, you can position each point cloud in a global coordinate system in real time with high accuracy during measurement. In Japan, receivers compatible with the quasi-zenith satellite "Michibiki" centimeter-level augmentation service (CLAS) can achieve positioning with errors of a few centimeters without installing a base station. Mounting an RTK-equipped camera on a drone improves the absolute accuracy of photogrammetry point clouds, and pairing an external RTK receiver with a smartphone enables point cloud scans with minimal positional drift. High-precision positioning technology suppresses cumulative errors from reference points during wide-area measurements, making long-distance point cloud distortion or drift nearly zero.

● Smartphone LiDAR and the latest methods: Recently, smartphone-embedded LiDAR has attracted attention and contributes significantly to the trend toward higher precision. Although built-in LiDAR in smartphones and tablets is inferior to professional equipment in terms of measurement range and point density, performance is improving yearly and already shows practical accuracy at short ranges. For example, one evaluation reported approximately ±5 cm (±2.0 in) error from models generated from iPhone and iPad LiDAR scans (under the same conditions TLS produced about ±3 mm (±0.12 in)). In another case, scanning an indoor depth of about 6.6 m (about 21.7 ft) with a smartphone resulted in a difference from the actual measurement of about 41 mm (about 1.61 in) (error 0.6%), confirming accuracy comparable to traditional laser distance meters. While smartphone LiDAR accuracy varies by situation, with proper techniques it is said that accuracy on the order of 1 cm (half-inch accuracy) can be achieved. In practice, scanning terrain with a tablet LiDAR and comparing it to drone surveying produced a volume difference of less than 0.1%, an extremely high-precision result. This indicates that handheld devices, not just expensive dedicated equipment, can approach near-zero error with the right usage. However, standalone smartphone scans tend to drift gradually over wide areas, so combining them with the previously mentioned high-precision GNSS helps compensate weaknesses and secures more stable positioning accuracy.

● AI-based data processing and noise reduction: Software advances are also supporting precision improvements. AI-based point cloud processing software is emerging, enabling automatic removal of unnecessary points and automatic extraction of ground surfaces from large point cloud datasets. For example, when calculating volumes, if AI can automatically classify and remove points that are not part of the measurement target—such as trees or heavy machinery—it prevents incorrect region selection by humans and leads to accurate earthwork quantity calculations. Filtering to remove noise and outlier points and smoothing surfaces also reduces variance in volume calculations. Additionally, cloud sharing and real-time processing of point cloud data have progressed. Services that integrate and process large point clouds in the cloud at high speed are increasing, enabling high-precision analysis results to be obtained immediately after scanning on site. With these latest software technologies, even users without specialized knowledge in point cloud surveying can obtain automatically precision-controlled data.

By leveraging these latest technologies, errors in point cloud–based volume calculations can be reduced to near zero. The evolution of hardware (high-precision sensors and GNSS) and software (AI processing and automated analysis) together make it possible to achieve both unprecedented accuracy and ease of use. The phrase "challenging zero error" is not an exaggeration—an era is approaching in which site management can grasp earthwork quantities at nearly the same level as actual measurements.

Simple Surveying with LRTK

As described above, 3D measurement using point cloud data brings great benefits in accuracy and efficiency for volume calculation. However, some may hesitate to adopt the latest technologies, worrying that in-house full implementation is difficult or that they lack the budget for expensive equipment. Here, attention should be paid to an approach called simple surveying using smartphone-based "LRTK." LRTK is a small RTK-GNSS receiver that can be attached to a smartphone, making centimeter-level positioning—which previously required specialized equipment—achievable with a smartphone per person. By attaching the dedicated unit to a smartphone and launching an app, you can perform 3D point cloud measurement while obtaining high-precision position information in real time. This combines the convenience of smartphone-embedded LiDAR or photogrammetry with RTK positioning accuracy, enabling anyone to perform high-precision 3D surveying easily.

Using simple surveying with LRTK, you can try acquiring 3D point cloud data and calculating volumes with the smartphone you already have, without immediately investing in an expensive laser scanner or drone. This lowers initial costs and worries about specialized knowledge while allowing you to enjoy the benefits of the latest "3D surveying × high-precision positioning" on site. Once tried on your own site, you will likely be impressed by the ease and accuracy. The new surveying style realized by LRTK is expected to spread as the new standard for site management. Experience this easy, high-precision volume calculation solution with LRTK—the world where you can grasp earthwork quantities with near-zero error is within reach.

FAQ

Q: How accurate is volume calculation using point clouds? A: It depends on the equipment and methods used, but generally point cloud–based volume calculation is more accurate than traditional manual methods. High-performance laser scanners can model with errors of several millimeters, and drone photogrammetry can achieve accuracy within several centimeters with appropriate techniques. Smartphone LiDAR scans have also produced cases where volumes were calculated with 1–2 cm accuracy under favorable conditions. Overall, with the latest technologies, extremely high accuracy such as less than 1% error is achievable.

Q: Do I need special equipment to acquire point cloud data? A: Not necessarily—you can get started without expensive equipment. While high-performance laser scanners and RTK-equipped drones are ideal for pursuing the highest accuracy, smartphones and tablets can acquire short-range point clouds using built-in LiDAR or cameras. Recently, small RTK receivers that attach to smartphones (for example, LRTK devices) have appeared, turning your phone into a high-precision surveying tool. You can adopt technologies in stages according to budget and application, so it’s recommended to try point cloud measurement with familiar devices first.

Q: Can a beginner handle point cloud volume calculation? A: Yes. Even without specialized knowledge, it is relatively easy to handle. Point cloud viewers and similar software increasingly offer intuitive 3D data displays and one-click volume calculation for selected regions. Even those without surveying or 3D CAD experience can obtain results in a short time once they learn the basic steps. Cloud-based point cloud services also eliminate the need for installation—upload your data and it will be analyzed automatically. Start with a small area to get used to it, and gradually expand your scope. Using simple surveying solutions like LRTK, you can truly experience "volume calculation anyone can do."

Q: What is "simple surveying with LRTK"? A: Simple surveying with LRTK refers to using a small RTK-GNSS receiver called "LRTK" that attaches to a smartphone, together with a dedicated app, to perform high-precision 3D surveying easily. This solution enables centimeter-level positioning and point cloud measurement—previously requiring specialized equipment and advanced skills—using only a smartphone. The LRTK device dramatically improves smartphone positional accuracy, allowing immediate calculation of distances, areas, and volumes from acquired point cloud data. Even without an expensive laser scanner, LRTK enables simple, high-precision on-site volume calculation.