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市场调查报告书
商品编码
1822390

2032 年 3D 牙科扫描仪市场预测：按产品类型、扫描器类型、技术、应用、最终用户和地区进行的全球分析

3D Dental Scanners Market Forecasts to 2032 - Global Analysis By Product Type, Scanner Type, Technology, Application, End User, and By Geography
出版日期: | 出版商: Stratistics Market Research Consulting | 英文 200+ Pages | 商品交期: 2-3个工作天内

价格

根据 Stratistics MRC 的数据，全球 3D 牙科扫描仪市场预计在 2025 年达到 21.5 亿美元，到 2032 年将达到 50 亿美元，预测期内的复合年增长率为 12.8%。

3D牙科扫描仪是现代牙科领域的革命性工具，能够创造出牙齿、牙龈和口腔结构的精确数位影像。它们利用雷射或光学扫描方法，取代传统的印模，从而实现更快、更准确、更方便患者的诊疗过程。采集的数据可建立详细的数位模型，有助于诊断、治疗计划以及牙冠、植入、牙桥和矫正器等牙科解决方案的製作，从而确保牙科手术的精准度、效率，并全面提升患者体验。

美容牙科的需求不断增长

人们越来越重视脸部美观和笑容的提升，这推动了对先进牙科影像处理解决方案的需求。越来越多的患者选择美容手术，例如贴面、矫正器和植入，这些手术需要精确的数位印模。 3D牙科扫描仪正成为个人化治疗方案和高精度修復的必备工具。诊所正在利用这些技术来减少患者就诊时间并提高患者满意度。社群媒体的兴起和注重美学的消费行为进一步激发了人们对数位牙科的兴趣。随着工作流程的数位化不断提高，注重美学的治疗正成为扫描器应用的主要成长动力。

缺乏意识和培训

许多牙科专业人士缺乏操作3D扫描仪并将其融入临床实践的正规训练。规模较小的诊所面临提升员工技能和管理CAD/CAM系统相关学习曲线的挑战。缺乏标准化的课程和认证课程减缓了市场渗透。此外，对成本和复杂性的误解阻碍了对数位化工具的投资。透过有针对性的教育和研讨会来弥补这一差距，对于释放更广泛的市场潜力至关重要。

整合人工智慧和机器学习

机器学习演算法正在增强影像解读能力，从而能够及早发现口腔内病变和异常。预测分析正被用于模拟治疗结果并优化修復设计。云端基础平台正在促进实验室和诊所之间的即时协作，从而提高工作流程效率。新兴趋势包括人工智慧驱动的扫描检验以及牙冠和牙桥的自动边缘检测。随着法律规范的不断发展，人工智慧的整合将重新定义数位化牙科的精准度和个人化。

激烈的竞争和价格压力

现有企业面临着透过创新实现差异化并保持盈利的压力。价格敏感地区青睐价格实惠的机型，而高端品牌则面临证明自身价值的挑战。科技的快速更新换代和产品频繁升级给采购週期带来了压力。分销商和诊所正在协商更高的利润率，这影响了供应商的永续性。

COVID-19的影响

疫情扰乱了常规牙科护理，推迟了择期牙科手术，并降低了诊所扫描仪的使用率。供应链中断影响了硬体可得性，并减缓了全球市场的采用。然而，这场危机加速了数位化，诊所纷纷采用非接触式工作流程和远距咨询。 3D扫描仪在减少实体印模和加强卫生通讯协定发挥了关键作用。监管机构加快了数位化工具的核准，以支持牙科诊所的安全復工。后疫情时代策略如今强调牙科成像系统的弹性、自动化和云端基础的互通性。

口内扫描器 (IOS) 市场预计将成为预测期内最大的市场

口内扫描器 (IOS) 细分市场预计将在预测期内占据最大市场份额，因为它在椅旁诊断和修復工作流程中发挥核心作用。 IOS 设备提供高解析度成像、即时视觉化以及与 CAD/CAM 系统的无缝整合。其人体工学设计和易用性正推动全科医生和专科医生对其的广泛采用。无线连接和人工智慧辅助扫描等技术进步正在提高临床效率。对当日牙科治疗和数位化印模的需求日益增长，这巩固了 IOS 的主导地位。随着扫描器精确度和速度的提升，IOS 将继续引领牙医诊所的数位转型。

牙科诊所部门预计将在预测期内实现最高的复合年增长率

预计在预测期内，牙科诊所细分市场将实现最高成长率，这得益于数位化的提高和以患者为中心的医疗模式的推进。牙科诊所正在投资3D扫描仪，以简化工作流程、缩短週转时间并改善治疗效果。美容和矫正治疗的兴起推动了诊所对精密影像处理工具的需求。与云端基础平台和数位实验室的整合正在提高营运灵活性。新兴趋势包括基于订阅的扫描器模型以及为小型诊所量身定制的捆绑软体解决方案。随着诊所不断现代化并扩展其服务范围，它们在推动扫描器普及方面的作用正变得越来越重要。

比最大的地区

由于快速的都市化和牙科基础设施的扩张，预计亚太地区将在预测期内占据最大的市场份额。中国、印度和韩国等国正在加大对数位医疗和牙科现代化的投资。政府正在倡议推动口腔清洁用品领域的国产化和技术应用。该地区越来越多地采用人工智慧诊断和行动扫描设备，以覆盖医疗资源匮乏的人群。全球原始设备製造商 (OEM) 与本地经销商之间的策略合作伙伴关係正在加速市场渗透。

复合年增长率最高的地区：

预计北美将在预测期内实现最高的复合年增长率，这得益于其在牙科创新和数位化整合领域的领先地位。美国和加拿大在采用人工智慧扫描仪和云端基础影像处理平台方面处于领先地位。监管机构正在简化设备核准流程，以促进下一代技术更快的商业化。牙科服务组织 (DSO) 正在扩大扫描器在多站点网路中的部署。关键进展包括与诊所管理软体的互通性和即时实验室整合。

免费客製化服务：

此报告的订阅者可以选择以下免费自订选项之一：

  • 公司简介
    • 对最多三家其他市场公司进行全面分析
    • 主要企业的SWOT分析（最多3家公司）
  • 区域细分
    • 根据客户兴趣对主要国家进行的市场估计、预测和复合年增长率（註：基于可行性检查）
  • 竞争基准化分析
    • 根据产品系列、地理分布和策略联盟对主要企业基准化分析

目录

第一章执行摘要

第二章 前言

  • 概述
  • 相关利益者
  • 调查范围
  • 调查方法
    • 资料探勘
    • 数据分析
    • 数据检验
    • 研究途径
  • 研究材料
    • 主要研究资料
    • 次级研究资讯来源
    • 先决条件

第三章市场走势分析

  • 驱动程式
  • 抑制因素
  • 机会
  • 威胁
  • 产品分析
  • 技术分析
  • 应用分析
  • 最终用户分析
  • 新兴市场
  • COVID-19的影响

第四章 波特五力分析

  • 供应商的议价能力
  • 买方的议价能力
  • 替代品的威胁
  • 新进入者的威胁
  • 竞争对手之间的竞争

第五章全球 3D 牙科扫描器市场（依产品类型）

  • 口内扫描器（IOS）
  • 手持式扫描仪
  • 锥状射束电脑断层扫描（CBCT）
  • 实验室扫描仪
  • 其他产品类型

6. 全球 3D 牙科扫描器市场（按扫描器类型）

  • 3D牙科光学扫描仪
  • 3D牙科雷射扫描仪

7. 全球3D牙科扫描器市场（按技术）

  • 结构光扫描仪
  • 雷射扫描仪

8. 全球3D牙科扫描器市场（按应用）

  • 修復牙科
  • 正畸
  • 义肢
  • 诊断和数位记录
  • 植入
  • 其他用途

9. 全球3D牙科扫描器市场（按最终用户）

  • 牙医诊所
  • 医院
  • 牙体技术所
  • 学术研究机构
  • 其他最终用户

9. 全球3D牙科扫描器市场（按地区）

  • 北美洲
    • 美国
    • 加拿大
    • 墨西哥
  • 欧洲
    • 德国
    • 英国
    • 义大利
    • 法国
    • 西班牙
    • 其他欧洲国家
  • 亚太地区
    • 日本
    • 中国
    • 印度
    • 澳洲
    • 纽西兰
    • 韩国
    • 其他亚太地区
  • 南美洲
    • 阿根廷
    • 巴西
    • 智利
    • 南美洲其他地区
  • 中东和非洲
    • 沙乌地阿拉伯
    • 阿拉伯聯合大公国
    • 卡达
    • 南非
    • 其他中东和非洲地区

第十一章 重大进展

  • 协议、伙伴关係、合作和合资企业
  • 收购与合併
  • 新产品发布
  • 业务扩展
  • 其他关键策略

第十二章 公司概况

  • 3Shape A/S
  • Shining 3D
  • Align Technology Inc.
  • Argen Corporation
  • Dentsply Sirona
  • Midmark Corporation
  • Carestream Dental LLC
  • Dental Wings Inc.
  • Planmeca Oy
  • BioHorizons IPH, Inc.
  • Medit Corp.
  • GC Corporation
  • Straumann Group
  • Vatech Co., Ltd.
  • Envista Holdings Corporation
Product Code: SMRC31144

According to Stratistics MRC, the Global 3D Dental Scanners Market is accounted for $2.15 billion in 2025 and is expected to reach $5.00 billion by 2032 growing at a CAGR of 12.8% during the forecast period. Three-dimensional dental scanners are innovative tools in modern dentistry that create precise digital images of teeth, gums, and mouth structures. Utilizing laser or optical scanning methods, they replace conventional impressions, making the process quicker, accurate, and more patient-friendly. The captured data produces detailed digital models that aid in diagnosis, treatment planning, and crafting dental solutions like crowns, implants, bridges, and orthodontic devices, ensuring improved accuracy, efficiency, and overall patient experience in dental procedures.

Market Dynamics:

Driver:

Increasing demand for aesthetic and cosmetic dentistry

The growing emphasis on facial aesthetics and smile enhancement is fueling demand for advanced dental imaging solutions. Patients are increasingly opting for cosmetic procedures such as veneers, aligners, and implants, which require precise digital impressions. 3D dental scanners are becoming essential tools for personalized treatment planning and high-accuracy restorations. Clinics are leveraging these technologies to reduce chair time and improve patient satisfaction. The rise of social media and beauty-conscious consumer behavior is further amplifying interest in digital dentistry. As workflows become more digitized, aesthetic-driven care is emerging as a key growth catalyst for scanner adoption.

Restraint:

Lack of awareness and training

Many dental professionals lack formal training in operating 3D scanners and integrating them into clinical routines. Smaller clinics face challenges in upskilling staff and managing the learning curve associated with CAD/CAM systems. The absence of standardized curricula and certification programs slows down market penetration. Additionally, misconceptions around cost and complexity deter investment in digital tools. Bridging this gap through targeted education and hands-on workshops is critical to unlocking broader market potential.

Opportunity:

Integration of AI and machine learning

Machine learning algorithms are enhancing image interpretation, enabling early detection of oral pathologies and anomalies. Predictive analytics are being used to simulate treatment outcomes and optimize prosthetic designs. Cloud-based platforms are facilitating real-time collaboration between labs and clinics, improving workflow efficiency. Emerging trends include AI-powered scan validation and automated margin detection for crowns and bridges. As regulatory frameworks evolve, AI integration is poised to redefine precision and personalization in digital dentistry.

Threat:

Intense competition and price pressure

Established players are under pressure to differentiate through innovation while maintaining profitability. Price-sensitive regions are favouring budget-friendly models, challenging premium brands to justify value. Rapid technological obsolescence and frequent product upgrades are straining procurement cycles. Distributors and clinics are negotiating harder on margins, impacting vendor sustainability.

Covid-19 Impact

The pandemic disrupted routine dental care, delaying elective procedures and reducing scanner utilization in clinics. Supply chain interruptions affected hardware availability and slowed installations across global markets. However, the crisis accelerated digital adoption, with clinics embracing contactless workflows and remote consultations. 3D scanners played a pivotal role in minimizing physical impressions and enhancing hygiene protocols. Regulatory bodies fast-tracked approvals for digital tools to support safe reopening of dental practices. Post-COVID strategies now emphasize resilience, automation, and cloud-based interoperability in dental imaging systems.

The intraoral scanners (IOS) segment is expected to be the largest during the forecast period

The intraoral scanners (IOS) segment is expected to account for the largest market share during the forecast period, due to their central role in chairside diagnostics and restorative workflows. IOS devices offer high-resolution imaging, real-time visualization, and seamless integration with CAD/CAM systems. Their ergonomic design and ease of use are driving adoption among general practitioners and specialists alike. Technological advancements such as wireless connectivity and AI-assisted scanning are enhancing clinical efficiency. The growing demand for same-day dentistry and digital impressions is reinforcing IOS dominance. As scanner accuracy and speed improve, IOS continues to lead the digital transformation in dental practices.

The dental clinics segment is expected to have the highest CAGR during the forecast period

Over the forecast period, the dental clinics segment is predicted to witness the highest growth rate, due to increasing digitization and patient-centric care models. Clinics are investing in 3D scanners to streamline workflows, reduce turnaround times, and improve treatment outcomes. The rise of cosmetic dentistry and orthodontics is boosting demand for precise imaging tools at the clinic level. Integration with cloud-based platforms and digital labs is enhancing operational agility. Emerging trends include subscription-based scanner models and bundled software solutions tailored for small practices. As clinics modernize and expand service offerings, their role in driving scanner adoption becomes increasingly pivotal.

Region with largest share:

During the forecast period, the Asia Pacific region is expected to hold the largest market share due to rapid urbanization and expanding dental infrastructure. Countries like China, India, and South Korea are witnessing increased investment in digital healthcare and dental modernization. Government initiatives are promoting domestic manufacturing and technology adoption in oral care. The region is embracing AI-driven diagnostics and mobile scanning units to reach underserved populations. Strategic collaborations between global OEMs and local distributors are accelerating market penetration.

Region with highest CAGR:

Over the forecast period, the North America region is anticipated to exhibit the highest CAGR, owing to its leadership in dental innovation and digital integration. The U.S. and Canada are at the forefront of adopting AI-enhanced scanners and cloud-based imaging platforms. Regulatory bodies are streamlining device approvals, encouraging faster commercialization of next-gen technologies. Dental service organizations (DSOs) are scaling scanner deployment across multi-location networks. Key developments include interoperability with practice management software and real-time lab collaboration.

Key players in the market

Some of the key players profiled in the 3D Dental Scanners Market include 3Shape A/S, Shining 3D, Align Technology Inc., Argen Corporation, Dentsply Sirona, Midmark Corporation, Carestream Dental LLC, Dental Wings Inc., Planmeca Oy, BioHorizons IPH, Inc., Medit Corp., GC Corporation, Straumann Group, Vatech Co., Ltd., and Envista Holdings Corporation.

Key Developments:

In June 2025, 3Shape has partnered with Eon Dental, a full-service clear aligner company, to strengthen Eon's clear aligner workflows with 3Shape's advanced digital solutions. This new strategic partnership reflects both companies' shared goal of driving innovation and making clear aligner treatment more accessible.

In March 2025, DENTSPLY SIRONA Inc. announced that the Company will participate in the Leerink Partners Global Healthcare Conference. Management is scheduled to present on Tuesday, March 11, 2025, at 3:00 pm ET.

Product Types Covered:

  • Introduction
  • Intraoral Scanners (IOS)
  • Hand-held Scanners
  • Cone Beam Computed Tomography (CBCT)
  • Laboratory Scanners
  • Other Product Types

Scanner Types Covered:

  • 3D Dental Light Scanners
  • 3D Dental Laser Scanners

Technologies Covered:

  • Structured Light Scanners
  • Laser Scanners

Applications Covered:

  • Restorative Dentistry
  • Orthodontics
  • Prosthodontics
  • Diagnostics & Digital Records
  • Implantology
  • Other Applications

End Users Covered:

  • Dental Clinics
  • Hospitals
  • Dental Laboratories
  • Academic & Research Institutions
  • Other End Users

Regions Covered:

  • North America
    • US
    • Canada
    • Mexico
  • Europe
    • Germany
    • UK
    • Italy
    • France
    • Spain
    • Rest of Europe
  • Asia Pacific
    • Japan
    • China
    • India
    • Australia
    • New Zealand
    • South Korea
    • Rest of Asia Pacific
  • South America
    • Argentina
    • Brazil
    • Chile
    • Rest of South America
  • Middle East & Africa
    • Saudi Arabia
    • UAE
    • Qatar
    • South Africa
    • Rest of Middle East & Africa

What our report offers:

  • Market share assessments for the regional and country-level segments
  • Strategic recommendations for the new entrants
  • Covers Market data for the years 2024, 2025, 2026, 2028, and 2032
  • Market Trends (Drivers, Constraints, Opportunities, Threats, Challenges, Investment Opportunities, and recommendations)
  • Strategic recommendations in key business segments based on the market estimations
  • Competitive landscaping mapping the key common trends
  • Company profiling with detailed strategies, financials, and recent developments
  • Supply chain trends mapping the latest technological advancements

Free Customization Offerings:

All the customers of this report will be entitled to receive one of the following free customization options:

  • Company Profiling
    • Comprehensive profiling of additional market players (up to 3)
    • SWOT Analysis of key players (up to 3)
  • Regional Segmentation
    • Market estimations, Forecasts and CAGR of any prominent country as per the client's interest (Note: Depends on feasibility check)
  • Competitive Benchmarking
    • Benchmarking of key players based on product portfolio, geographical presence, and strategic alliances

Table of Contents

1 Executive Summary

2 Preface

  • 2.1 Abstract
  • 2.2 Stake Holders
  • 2.3 Research Scope
  • 2.4 Research Methodology
    • 2.4.1 Data Mining
    • 2.4.2 Data Analysis
    • 2.4.3 Data Validation
    • 2.4.4 Research Approach
  • 2.5 Research Sources
    • 2.5.1 Primary Research Sources
    • 2.5.2 Secondary Research Sources
    • 2.5.3 Assumptions

3 Market Trend Analysis

  • 3.1 Introduction
  • 3.2 Drivers
  • 3.3 Restraints
  • 3.4 Opportunities
  • 3.5 Threats
  • 3.6 Product Analysis
  • 3.7 Technology Analysis
  • 3.8 Application Analysis
  • 3.9 End User Analysis
  • 3.10 Emerging Markets
  • 3.11 Impact of Covid-19

4 Porters Five Force Analysis

  • 4.1 Bargaining power of suppliers
  • 4.2 Bargaining power of buyers
  • 4.3 Threat of substitutes
  • 4.4 Threat of new entrants
  • 4.5 Competitive rivalry

5 Global 3D Dental Scanners Market, By Product Type

  • 5.1 Introduction
  • 5.2 Intraoral Scanners (IOS)
  • 5.3 Hand-held Scanners
  • 5.4 Cone Beam Computed Tomography (CBCT)
  • 5.5 Laboratory Scanners
  • 5.6 Other Product Types

6 Global 3D Dental Scanners Market, By Scanner Type

  • 6.1 Introduction
  • 6.2 3D Dental Light Scanners
  • 6.3 3D Dental Laser Scanners

7 Global 3D Dental Scanners Market, By Technology

  • 7.1 Introduction
  • 7.2 Structured Light Scanners
  • 7.3 Laser Scanners

8 Global 3D Dental Scanners Market, By Application

  • 8.1 Introduction
  • 8.2 Restorative Dentistry
  • 8.3 Orthodontics
  • 8.4 Prosthodontics
  • 8.5 Diagnostics & Digital Records
  • 8.6 Implantology
  • 8.7 Other Applications

9 Global 3D Dental Scanners Market, By End User

  • 9.1 Introduction
  • 9.2 Dental Clinics
  • 9.3 Hospitals
  • 9.4 Dental Laboratories
  • 9.5 Academic & Research Institutions
  • 9.6 Other End Users

9 Global 3D Dental Scanners Market, By Geography

  • 9.1 Introduction
  • 9.2 North America
    • 9.2.1 US
    • 9.2.2 Canada
    • 9.2.3 Mexico
  • 9.3 Europe
    • 9.3.1 Germany
    • 9.3.2 UK
    • 9.3.3 Italy
    • 9.3.4 France
    • 9.3.5 Spain
    • 9.3.6 Rest of Europe
  • 9.4 Asia Pacific
    • 9.4.1 Japan
    • 9.4.2 China
    • 9.4.3 India
    • 9.4.4 Australia
    • 9.4.5 New Zealand
    • 9.4.6 South Korea
    • 9.4.7 Rest of Asia Pacific
  • 9.5 South America
    • 9.5.1 Argentina
    • 9.5.2 Brazil
    • 9.5.3 Chile
    • 9.5.4 Rest of South America
  • 9.6 Middle East & Africa
    • 9.6.1 Saudi Arabia
    • 9.6.2 UAE
    • 9.6.3 Qatar
    • 9.6.4 South Africa
    • 9.6.5 Rest of Middle East & Africa

11 Key Developments

  • 11.1 Agreements, Partnerships, Collaborations and Joint Ventures
  • 11.2 Acquisitions & Mergers
  • 11.3 New Product Launch
  • 11.4 Expansions
  • 11.5 Other Key Strategies

12 Company Profiling

  • 12.1 3Shape A/S
  • 12.2 Shining 3D
  • 12.3 Align Technology Inc.
  • 12.4 Argen Corporation
  • 12.5 Dentsply Sirona
  • 12.6 Midmark Corporation
  • 12.7 Carestream Dental LLC
  • 12.8 Dental Wings Inc.
  • 12.9 Planmeca Oy
  • 12.10 BioHorizons IPH, Inc.
  • 12.11 Medit Corp.
  • 12.12 GC Corporation
  • 12.13 Straumann Group
  • 12.14 Vatech Co., Ltd.
  • 12.15 Envista Holdings Corporation

List of Tables

  • Table 1 Global 3D Dental Scanners Market Outlook, By Region (2024-2032) ($MN)
  • Table 2 Global 3D Dental Scanners Market Outlook, By Product Type (2024-2032) ($MN)
  • Table 3 Global 3D Dental Scanners Market Outlook, By Intraoral Scanners (IOS) (2024-2032) ($MN)
  • Table 4 Global 3D Dental Scanners Market Outlook, By Hand-held Scanners (2024-2032) ($MN)
  • Table 5 Global 3D Dental Scanners Market Outlook, By Cone Beam Computed Tomography (CBCT) (2024-2032) ($MN)
  • Table 6 Global 3D Dental Scanners Market Outlook, By Laboratory Scanners (2024-2032) ($MN)
  • Table 7 Global 3D Dental Scanners Market Outlook, By Other Product Types (2024-2032) ($MN)
  • Table 8 Global 3D Dental Scanners Market Outlook, By Scanner Type (2024-2032) ($MN)
  • Table 9 Global 3D Dental Scanners Market Outlook, By 3D Dental Light Scanners (2024-2032) ($MN)
  • Table 10 Global 3D Dental Scanners Market Outlook, By 3D Dental Laser Scanners (2024-2032) ($MN)
  • Table 11 Global 3D Dental Scanners Market Outlook, By Technology (2024-2032) ($MN)
  • Table 12 Global 3D Dental Scanners Market Outlook, By Structured Light Scanners (2024-2032) ($MN)
  • Table 13 Global 3D Dental Scanners Market Outlook, By Laser Scanners (2024-2032) ($MN)
  • Table 14 Global 3D Dental Scanners Market Outlook, By Application (2024-2032) ($MN)
  • Table 15 Global 3D Dental Scanners Market Outlook, By Restorative Dentistry (2024-2032) ($MN)
  • Table 16 Global 3D Dental Scanners Market Outlook, By Orthodontics (2024-2032) ($MN)
  • Table 17 Global 3D Dental Scanners Market Outlook, By Prosthodontics (2024-2032) ($MN)
  • Table 18 Global 3D Dental Scanners Market Outlook, By Diagnostics & Digital Records (2024-2032) ($MN)
  • Table 19 Global 3D Dental Scanners Market Outlook, By Implantology (2024-2032) ($MN)
  • Table 20 Global 3D Dental Scanners Market Outlook, By Other Applications (2024-2032) ($MN)
  • Table 21 Global 3D Dental Scanners Market Outlook, By End User (2024-2032) ($MN)
  • Table 22 Global 3D Dental Scanners Market Outlook, By Dental Clinics (2024-2032) ($MN)
  • Table 23 Global 3D Dental Scanners Market Outlook, By Hospitals (2024-2032) ($MN)
  • Table 24 Global 3D Dental Scanners Market Outlook, By Dental Laboratories (2024-2032) ($MN)
  • Table 25 Global 3D Dental Scanners Market Outlook, By Academic & Research Institutions (2024-2032) ($MN)
  • Table 26 Global 3D Dental Scanners Market Outlook, By Other End Users (2024-2032) ($MN)

Note: Tables for North America, Europe, APAC, South America, and Middle East & Africa Regions are also represented in the same manner as above.