Image Based Modeling and Rendering: Exploring Visual Realism: Techniques in Computer Vision

By Fouad Sabry

What is Image Based Modeling and Rendering

In computer graphics and computer vision, image-based modeling and rendering (IBMR) methods rely on a set of two-dimensional images of a scene to generate a three-dimensional model and then render some novel views of this scene.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Image-based modeling and rendering

Chapter 2: 2D computer graphics

Chapter 3: 3D projection

Chapter 4: Light field

Chapter 5: View synthesis

Chapter 6: Autoencoder

Chapter 7: Structure tensor

Chapter 8: Segmentation-based object categorization

Chapter 9: 2D to 3D conversion

Chapter 10: Variational autoencoder

(II) Answering the public top questions about image based modeling and rendering.

(III) Real world examples for the usage of image based modeling and rendering in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Image Based Modeling and Rendering.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 5, 2024

Book preview

Chapter 1: Image-based modeling and rendering

In computer graphics and computer vision, image-based modeling and rendering (IBMR) techniques use a collection of two-dimensional photographs of a scene to produce a three-dimensional model and then render some innovative views of this scene.

Using the conventional method of computer graphics, a three-dimensional geometric model has been created and reprojected onto a two-dimensional image. In contrast, computer vision is primarily concerned with recognizing, grouping, and extracting features (edges, faces, etc.) from a given image and then attempting to interpret them as three-dimensional information. Image-based modeling and rendering enables the use of several two-dimensional photos to generate innovative two-dimensional images without the need for manual modeling.

Instead of evaluating a solid's physical model alone, IBMR approaches typically emphasize light modeling more.

IBMR is predicated on the plenoptic illumination function, which is a parameterization of the light field.

The plenoptic function describes the light rays contained within a particular volume.

It can be represented with seven dimensions: a ray is defined by its position (x,y,z) , its orientation (\theta ,\phi ) , its wavelength (\lambda ) and its time (t) : P(x,y,z,\theta ,\phi ,\lambda ,t) .

IBMR approaches attempt to approximate the plenoptic function in order to create a novel set of two-dimensional images from another two-dimensional image set.

Given the function's high dimensionality, practical techniques impose restrictions on the parameters to lower this number (typically to 2 to 4).

View morphing generates a picture transition.

Panoramic imaging creates panoramas by combining separate still photos into mosaics.

Lumigraph is dependent upon a dense sampling of a scene.

Space carving creates a three-dimensional model based on a photo-consistency analysis.

{End Chapter 1}

Chapter 2: 2D computer graphics

Generating digital images on a computer, typically from two-dimensional models (such as 2D geometric models, text, and digital images) and using methods tailored to these types of models is known as 2D computer graphics. Either the models themselves or the field of computer science that includes them could be meant.

Typography, cartography, technical drawing, advertising, etc. are all examples of applications that built on the foundation of 2D computer graphics. Two-dimensional models are preferred over three-dimensional computer graphics in these cases because they allow for greater direct control over the image. This is because the two-dimensional image is more than just a representation of a real-world object; it also has additional semantic value (whose approach is more akin to photography than to typography).

Document descriptions based on 2D computer graphics techniques can be significantly smaller than the corresponding digital image in many fields, including desktop publishing, engineering, and business. Since this representation can be rendered at varying resolutions to accommodate a variety of output devices, it is also more versatile. This is why 2D graphic files are commonly used for archiving and transporting documents and images.

Vector graphics devices from the 1950s paved the way for the first 2D computer graphics. In the decades that followed, raster-based devices became the norm. Two of the most important innovations in this area are the PostScript language and the X Window System protocol.

Combinations of geometric models (also known as vector graphics), digital images (also known as raster graphics), text to be typeset (described by its content, font style and size, color, position, and orientation), mathematical functions and equations, and other types of information are all possible in 2D graphics models. Two-dimensional geometric transformations, such as translation, rotation, and scaling, allow for easy and precise manipulation of these parts. An object with a self-rendering method, a process that arbitrarily assigns colors to image pixels, describes the image in object-oriented graphics. In object-oriented programming paradigms, complex models are constructed from submodels.

The principles of Euclidean geometry, In geometry, a translation moves every point by some fixed distance in some direction.

One type of rigid motion is translation; other types include rotation and reflection.

It is also possible to think of a translation as the process of adding a constant vector to each point, or as if the coordinate system's origin were moved.

A translation operator is an operator T_\mathbf{\delta} such that T_\mathbf{\delta} f(\mathbf{v}) = f(\mathbf{v}+\mathbf{\delta}).

When v is a constant vector, then the translation Tv will work as Tv(p) = p + v.

Theoretically, if T is a translation,, If A is a subset and T is a function, then the translation of A by T is the image of A under T.

The translation of A by Tv is often written A + v.

Any translation in a Euclidean space is also an isometry. The set of all translations is called the translation group T, and it is an ordinary subgroup of the Euclidean group E, being isomorphic to the space itself (n ). Orthogonal group O is an isomorphism of the quotient group E(n) by T. (n ):

E(n ) / T ≅ O(n ).

Unlike a linear transformation, a translation is an affine transformation, The translation operator is typically represented by a matrix, making it linear, when homogeneous coordinates are used.

Thus we write the 3-dimensional vector w = (wx, wy, wz) using 4 homogeneous coordinates as w = (wx, wy, wz, 1).

Each homogeneous vector p (in homogeneous coordinates) must be multiplied by this translation matrix if an object is to be translated by a vector v:

T_{\mathbf{v}} = \begin{bmatrix} 1 & 0 & 0 & v_x \\ 0 & 1 & 0 & v_y \\ 0 & 0 & 1 & v_z \\ 0 & 0 & 0 & 1 \end{bmatrix}

The product of the multiplication is as shown in the table below:

T_{\mathbf{v}} \mathbf{p} = \begin{bmatrix} 1 & 0 & 0 & v_x \\ 0 & 1 & 0 & v_y\\ 0 & 0 & 1 & v_z\\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} p_x \\ p_y \\ p_z \\ 1 \end{bmatrix} = \begin{bmatrix} p_x + v_x \\ p_y + v_y \\ p_z + v_z \\ 1 \end{bmatrix} = \mathbf{p} + \mathbf{v}

To find the inverse of a translation matrix, simply flip the vector's direction:

T^{-1}_{\mathbf{v}} = T_{-\mathbf{v}} . \!

Likewise, multiplying the vectors together yields the product of two translation matrices:

T_{\mathbf{u}}T_{\mathbf{v}} = T_{\mathbf{u}+\mathbf{v}} . \!

Multiplication of translation matrices is commutative because vector addition is commutative (unlike multiplication of arbitrary matrices).