From Pixels to 3D Shapes: An Overview of 3D Data Representations
Have you ever wondered how computers perceive and understand the three-dimensional world around us? From recognizing objects to reconstructing scenes,3D computer vision plays a crucial role in various applications. But how do computers represent and reason about complex 3D shapes? In this blog let’s explore the magic behind how computers perceive and reason about complex 3D shapes.
At the heart of this fascinating field lies 3D computer vision, a specialized branch of computer vision that focuses on understanding and processing three-dimensional visual data from the real world. By analyzing depth, shape, and spatial relationships in images and videos, 3D computer vision enables computers to interpret the 3D structure of objects and scenes with remarkable precision and accuracy.
Deep Learning architectures have demonstrated impressive capabilities in analyzing 2D data, but the same success was not easily replicated in the 3D domain. One of the key reasons behind this disparity was the considerable demand for a large amount of training data, which was particularly challenging to obtain for 3D tasks.
Advancements in structured-light 3D scanners, time-of-flight cameras, and other affordable 3D-data acquisition devices have led to a significant increase in the availability of 3D data. These advancements have brought about a wealth of information about the full geometry of 3D objects and scenes, empowering the field of 3D computer vision
Raw 3D data captured by different scanning devices come in different forms that vary in both, the structure and the properties. 3D data is categorized mainly into two main families:- Euclidean-structured data and non-Euclidean data.
Euclidean data
Euclidean-structured data in the context of 3D computer vision refers to representations with a well-defined grid structure, where properties such as a global parametrization and a common system of coordinates are preserved.
These properties make extending the already-existing 2D DeepLearning approaches to 3D data a straightforward task, where the convolution operation is kept the same as 2D. 3D Euclidean data is more suitable for analyzing rigid objects where the deformations are minimal.
For example, in medicine, MRI scans use 3D Euclidean grids to analyze complex anatomical structures. In robotics and manufacturing, voxel data is commonly used to model and simulate rigid objects. The main 3D data representations that fall under this category are as follows :-
a) Descriptors :- Shape descriptors are like simplified representations of 3D objects used to describe their geometric or topological characteristics. They capture information about the object’s shape, surface, texture, and more. These descriptors can be broadly classified into two categories:
- Global Descriptors:
- Global descriptors give a brief but informative description of the entire 3D object.
- Example: Imagine describing a house’s overall shape, including its roof, walls, and windows.
2. Local Descriptors:
- Local descriptors focus on smaller parts or patches of the 3D object, providing more detailed information.
- Example: Instead of describing the whole house, local descriptors might highlight specific features like the front door or chimney.
Shape descriptors help computers recognize objects, find similarities between shapes, and enable efficient processing of complex 3D data.
b) RGB-D data:- 3D data represented as RGB-D images has gained popularity due to sensors like Microsoft’s Kinect. RGB-D data combines 2D color information (RGB) with depth information (D) to give a 2.5D view of the captured 3D object.
For example, think of it as having a photo of a colorful object along with a depth map that shows how far each part of the object is from the camera.
These RGB-D images are both cost-effective and powerful, making them useful for various tasks. For example, it helps in recognizing objects by their appearance, predicting object poses, reconstructing scenes, and finding corresponding points in different views. This makes RGB-D data essential tool in the exciting world of 3D computer vision.
c) 3D Data Projections:- Representing 3D data through projections involves transforming 3D objects into 2D grids with specific features.
For example, imagine projecting a 3D object onto a flat surface, creating a 2D representation. This projected data retains important characteristics of the original shape.
Common projections include spherical and cylindrical representations, which are rotation-invariant around their main axis. However, for complex 3D computer vision tasks like dense correspondence (matching points between objects), these projections may not be ideal due to potential information loss during the process.
d) Volumetric Data :-Volumetric data uses voxels to create a regular grid in three-dimensional space, describing how the 3D object is distributed within the scene.
For example, Imagine voxels as tiny cubes that stack together to form the shape of an object in three-dimensional space.
Voxel-based representation is simple and can encode information about the 3D shape and its viewpoint. However, it has limitations. It represents both occupied and non-occupied parts of the scene, which requires a lot of memory storage. This makes voxel-based representation unsuitable for high-resolution data, where memory efficiency becomes crucial.
e) Multi-view data:- 3D data can be represented by combining several 2D images captured from different viewpoints of the same object. Think of it like taking pictures of an object from various angles. This representation helps reduce noise, deal with incomplete data, handle occlusions, and address lighting issues.
To learn from these 2D images and reconstruct the 3D shape, a function is used to model each view separately. Then, all the functions are optimized together to represent the complete 3D shape. It’s like putting together puzzle pieces from different pictures to understand the entire 3D scene.
Non-Euclidean Data
The second type of 3D data representation is non-Euclidean data. Unlike Euclidean data, it doesn’t have a global parametrization or a common coordinate system.
Also, non-Euclidean data lacks the simple structures and doesn’t follow a straightforward vector space pattern, making it challenging to directly apply 2D deep learning methods.
This means we need specialized approaches to effectively handle non-Euclidean data in the context of deep learning. Some common examples of non-Euclidean data include point clouds, 3D meshes, and graphs.
a) 3D Point Clouds:-A point cloud is an unstructured collection of 3D points that approximates the shape of an object. It’s considered non-Euclidean data because it lacks a global structure and doesn’t follow a straightforward coordinate system.
However, point clouds can be seen in two ways: as unstructured sets of 3D points (non-Euclidean) or as small subsets with global coordinates and invariance to transformations (Euclidean). The choice depends on whether we focus on their global or local features.
For complex tasks like recognition and matching, we treat point clouds as non-Euclidean data because most learning techniques aim to capture global features.
Despite being easy to capture using technologies like Kinect and structured light scanners, processing point clouds can be challenging due to their lack of structure and ambiguity in surface information.
b) 3D meshes and graphs :- 3D meshes are widely used to represent 3D shapes. They consist of faces (polygons) and vertices, describing how the mesh exists in 3D space. While the local geometry follows a grid-like structure (Euclidean), the global aspects lack well-defined Euclidean properties.
Learning 3D meshes is a challenge due to their irregular nature, making it difficult to apply deep learning methods directly. They often encounter noise, missing data, and resolution issues as well.
Another way to represent 3D meshes is by using graphs, where nodes represent vertices, and edges indicate connectivity. Analyzing graph spectral properties has paved the way for innovative approaches, such as defining convolution-like operations on graphs or meshes converted to graphs.
For example, imagine you want to create a 3D model of a human face using a mesh representation. The mesh is like a network of triangles and points that form the surface of the face in 3D space. While the individual triangles and points follow regular rules (Euclidean), understanding the entire mesh as a whole is more challenging because it’s irregular and lacks clear overall properties. To tackle this complexity, we have graph-based methods, which allow us to study and analyze the facial features in 3D space with greater efficiency.
Limitations of Traditional 3D Representations
Traditional explicit representations like point clouds, meshes, and voxels have been widely used for many years. One of the primary challenges with explicit representations is their inefficiency in handling complex and deformable 3D shapes. They often struggle with accurately capturing complex details and dealing with incomplete or noisy data.
For example, representing a human face as a point cloud or a mesh might work well for basic shape approximation, but it falls short when it comes to accurately capturing facial expressions, fine wrinkles, or minute details that define an individual’s unique appearance.
Similarly, voxel-based representations suffer from high memory requirements, making them impractical for representing high-resolution or large-scale 3D scenes.
Next Up: Exploring Occupancy Networks — Architecture, Mathematics, and Applications!
As traditional 3D representations showed their limitations, the demand for more powerful and robust techniques arose, leading to the emergence of advanced methods like Occupancy Networks. In my upcoming post, we’ll look into their architecture, mathematical foundations, and real-world applications. Stay tuned to uncover the magic behind Occupancy Networks and their impact on 3D shape representation!!
