Mastering 3D Computer Vision & Point Cloud Processing-Mod 3–Introduction to 2D-2.5D-3D Data

Introduction:

Welcome to the ✍️“3D Computer Vision & Point Cloud Processing Blog Series”. This series of blogs is your hands-on guide to mastering 3D point cloud processing with Python. In this post, we’ll explore “Introduction to 2D - 2.5D - 3D data”.

Topics to be discussed in this blog:

1. Brief Overview of 3D
2. 2D Data Introduction
3. 2.5D Data Introduction
4. 3D Data Introduction
5. 2D Data vs 2.5 Data vs 3D Data
6. Introduction to 3D Data Types
7. Differences among Different 3D Data Types
8. Advantages and Disadvantages of Different 3D Data Types

📚Brief Overview of 3D

Let’s Start a fascinating 3D Journey…

Imagine you’re standing in front of a beautiful statue. When you look at it from the front, you see its width and height, much like looking at a photograph — a representation in two dimensions. However, if you could walk around the statue, you would also perceive its depth, seeing it from different angles — front, back, sides, and even from above or below. This ability to view objects in three dimensions is at the heart of 3D computer vision.

Unlike traditional cameras that capture flat images, 3D computer vision utilizes sophisticated techniques to unlock a hidden dimension, allowing computers to perceive the depth, shape, and size of objects in the real world. Think of it as giving machines the ability to step off the screen and into reality.

Imagining this,

1. For example, think about how a self-driving car “sees” the road. It doesn’t just see a flat image; it perceives the depth of objects around it, enabling it to navigate safely. In virtual reality, 3D computer vision creates immersive experiences by simulating depth, making you feel like you’re in a different world. Even in healthcare, 3D imaging techniques help doctors visualize complex structures inside the body for more accurate diagnoses and treatment plans.
2. Robots in factories: Precisely manipulating delicate parts, navigating complex assembly lines, and even performing intricate repairs, all thanks to their newfound ability to “see” the three-dimensional world around them.
3. Robot chef in a restaurant kitchen: 3D vision allows it to not only “see” the ingredients on the counter but also accurately gauge their size, shape, and position. This enables the robot to precisely pick up a delicate egg or effortlessly lift a heavy pot, just like a skilled human chef.
4. Virtual reality: Stepping into immersive worlds that feel real, where you can not only see a virtual object but also reach out and interact with it, all thanks to the magic of 3D perception.

In essence, 3D computer vision expands the possibilities of technology in numerous fields, from robotics and gaming to healthcare and architecture. The potential applications are truly boundless. So, as we delve deeper into the world of 3D computer vision, remember that it’s not just about seeing in three dimensions; it’s about unlocking a new dimension of understanding and interaction with our surroundings.

2D Data Introduction

Imagine you’re looking at a photograph of a mountain. The image captures the width and height of the mountain, showing its shape and features. However, you can’t tell how far away the mountain is or how deep its valleys are. This is because the photograph is in 2D, representing only two dimensions. Examples of 2D and 3D data are,

• 2D Data (Image): A photograph of a mountain captures its width and height but lacks depth perception.
• 3D Data (Point Cloud, Mesh, Volumetric Data): A point cloud of a building captures the XYZ coordinates of each point, representing its three-dimensional shape.

2.5D Data Introduction

Definition of 2D, 2.5D, 3D:

1. 2D Data: 2D data refers to information captured and represented in two dimensions, typically width and height. Examples include images, and photographs.
2. 3D Data: 3D data represents information in three dimensions, encompassing width, height, and depth. Examples include point clouds, depth maps, volumetric data, and 3D models.
3. 2.5D Data: It is a representation of depth alongside width and height. It helps to generate 3D data such as point clouds using camera parameters.

Illustration of 2D, 2.5D, 3D:

1. 2D Data (Image): A photograph captures a mountain’s width and height while lacking depth.
2. 3D Data (Point Cloud): Imagine a point cloud generated from LiDAR scanning of the mountain. Each point in the cloud represents a specific location in 3D space, including x-coordinate, y-coordinate, and z-coordinate(depth).
3. 2.5D Data (Depth Map): A depth map of the mountain provides a 2.5D representation. It includes depth information alongside width and height but doesn’t offer a complete 3D model. For example, a depth map of a room indicates the distance of objects in the room from the depth camera but not a full 3D representation. Each depth value corresponds to a specific 2D coordinate (x, y) in the map, indicating the distance of that point from the depth camera. Note that each depth value is represented in 2D coordinates only. For example, at the (100, 200) location, the depth is 3.5meter.

In summary, 2D data captures width and height, 2.5D data captures depth map and 3D data represents points in 3D space. The images are taken from ‘Real-Time Refraction Through Deformable Objects’ http://dx.doi.org/10.1145/1230100.1230116

Left:2D view point of 3D Bunny data (Not 2D RGB), Right: Its Depth Map

Its 3D data (from a viewpoint)

How to generate 2.5D Data?

Depth maps can be captured using specialized depth cameras or computed from stereo images.

1. Depth map is captured by depth cameras including Intel Real sense, Azure Kinect (or)
2. Alternatively, they can be computed using two stereo images (RGB/Gray) capturing the same scene/object with two shifted cameras. These stereo images capture the same scene from slightly different angles, allowing algorithms to calculate the relative distance of objects from the camera. This information is then used to create a depth map, providing a 2.5D representation of the scene.

In depth maps, each (x, y) represents depth values in millimeters or meters. This depth map of size width x height is projected as a 3D point cloud using a projection matrix using depth camera parameters.

2.5D to 3D Conversion:

1. A 2.5D data (depth maps) can be converted to 3D point cloud data using depth camera’s intrinsic parameters, including focal length and distortion coefficients. (or)
2. Alternatively, the latest neural network methods can convert a depth map to 3D data.

2D to 3D Conversion:

Converting from 2D images to full 3D is generally not possible due to the lack of depth information. However, stereo images can be used to compute disparity maps, which are then converted to depth maps and subsequently to point cloud data using camera parameters or the latest neural networks estimate depth map from single 2D images. Other techniques, such as SLAM, can also compute 3D using a set of 2D images.

Case1: Given stereo image pair:

• A stereo pair can be used to compute a disparity map.
• The disparity map is converted to 2.5 D depth map using RGB camera parameters.
• This depth map is converted to a 3D point cloud using the depth camera’s parameters. Note that RGB camera parameters are not used for the 2.5D to 3D conversion.

Case2: Given only single RGB image:

• Latest neural network techniques, such as “Depth from a Single Image,” can estimate the depth map from a single RGB image.

3D Data Introduction

3D data represents information in three-dimensional coordinates, including width, height, and depth. Unlike both 2D images and 2.5D depth maps, which are typically sized in width x height and stored in JPG/PNG/… format, 3D data is not formatted in this way. Instead, it consists of a collection of 3D points represented as arrays in various file formats such as PCD and OBJ. 3D data is essentially a collection of individual points in 3D space, each with its own x, y, and z coordinates. These points come together to form a complete representation of an object or scene. Below is a sample of 3D point cloud data for illustration purposes.

Sample 3D Point Cloud Data

In future blogs, we will explore these file formats in greater detail.

2D Data vs 2.5 Data vs 3D Data

2D vs 2.5D vs 3D Comparison

Introduction to 3D Data Types

Primarily, there are three types of 3D data: point clouds, meshes, and volumetric data.

1. Point Clouds: Point clouds are a fundamental data type in 3D computer vision and represent surfaces as a collection of points in 3D space. Each point in a point cloud is defined by its x, y, and z coordinates, which specify its position in the 3D world. Additionally, points in a point cloud may include other attributes such as color, intensity, or surface normals, which provide further information about the object’s appearance and structure.
2. Meshes: A mesh is another common representation of 3D objects, defined by a set of vertices, edges, and faces. Vertices are points in 3D space, edges connect vertices, and faces are flat surfaces formed by connecting edges. Meshes are used to define the shape of an object’s surface with more detail than point clouds, as they can accurately represent the geometry of complex surfaces.
3. Volumetric Data: Volumetric data represents objects as a 3D grid, where each cell in the grid (voxel) contains information about the object’s properties at that point in space. This type of data is useful for representing objects that have volume, such as medical images of organs or industrial scans of machinery. Volumetric data can capture both the exterior surface and interior properties of objects, making it valuable for a wide range of applications.

Illustration:

The figures below show the different 3D data representations of the Bunny dataset.

Bunny Point Cloud Data (colored)

Bunny Mesh Data

Bunny Volumetric Data (colored)

1. Point Clouds: Imagine a 3D model of a car represented as a cloud of points, where each point corresponds to a specific location on the car’s surface. The points collectively define the shape and structure of the car in 3D space.
2. Meshes: Picture a wireframe model of a cube, where the vertices define the corners of the cube, the edges connect the vertices, and the faces complete the surface of the cube. This mesh representation accurately captures the shape of the cube.
3. Volumetric Data: Think of a 3D grid representing a human brain scan, where each voxel in the grid contains information about the brain’s properties at that point. The volumetric data provides a detailed representation of the brain’s structure and can be used for analysis and visualization.

Differences among Different 3D Data Types

This table summarizes the key characteristics, acquisition methods, and use cases of the three main 3D data types:

Different 3D Data Types Comparison

Key Differences:

• Sparsity/Density: Point clouds are sparse, meaning they contain fewer data points compared to meshes and volumetric data. Point clouds are the sparsest, followed by meshes, and volumetric data is the densest.
• Structure: Point clouds are unstructured, Meshes have a defined structure with defined relationships between data points and volumetric data are structured and organized in s grid-like structure.
• Information captured: Point clouds capture basic 3D coordinates, meshes capture surface details, and volumetric data captures both surface and interior details.
• Acquisition methods: LiDAR and cameras are commonly used for capturing point clouds, while scanning and modeling software are used for meshes, and CT and MRI scans are used for volumetric data.
• Applications: Point clouds are valuable in object recognition and robotics, meshes are essential for computer graphics and visualization, and volumetric data plays a crucial role in medical imaging and scientific visualization.

Selection of Data Types Based on Applications:

The choice of 3D data type depends on the specific application and the level of detail required.

• Point clouds: Ideal for capturing large, complex objects and efficient for initial analysis. Used for object recognition in self-driving cars, robotics, and scene understanding in augmented reality.
• Meshes: Well-suited for representing smooth, closed surfaces and commonly used in computer graphics and visualization. Widely used in computer graphics and animation for creating realistic 3D models, visualization applications, and even 3D printing.
• Volumetric data: Valuable in medical imaging and scientific simulations where understanding the internal properties of an object is crucial. Plays a crucial role in medical imaging for analyzing CT scans and MRIs, as well as in scientific visualization for studying complex structures and simulations.

Advantages and Disadvantages of Different 3D Data Types

When working with 3D data, different representation formats offer unique advantages and disadvantages. Understanding these characteristics can help in choosing the most suitable format for specific applications. Below is a comparison of three common types of 3D data representation: Point Clouds, Meshes, and Volumetric Data.

Advantages vs Disadvantages of Different 3D Data Types

In summary, each data type has its strengths and weaknesses. Point clouds offer direct 3D representation but can be sparse and challenging to process. Meshes provide accurate surfaces but come with a more complex data structure. Volumetric data represents entire volumes but requires considerable storage space. The choice of data type depends on the specific requirements of the application and the balance between accuracy, complexity, and resource requirements.

✨Happy exploring! Happy learning!✨

📝Next Blog Preview:

In the upcoming post, 🚀“Mastering 3D Computer Vision & Point Cloud Processing- Module 4–Interpreting 3D Point Cloud Data: An Illustration”.

Topics to be discussed in next blog:

1. Overview of 3D Data Acquisition
2. Different Types of Sensors used for Capturing 3D Data
3. Well-Known 3D Sensors
4. How Points are Organized in 3D Space

Topics to be discussed in the upcoming blogs- Immediate Focus:

• Different Formats for Storing Point Cloud Data
• Different Formats for Reading and writing the Point Cloud Data
• Choosing Point Cloud vs. Other 3D Data Types
• Explore 3D Metadata