\text{Image Formation and the Pinhole Camera}
\textbf{Naresh Kumar Devulapally}
\text{CSE 4/573: Computer Vision and Image Processing}
\text{Naresh Kumar Devulapally}
\text{May 29 2025}
\text{CSE 4/573: CVIP, Summer 2025}
\text{Lectures 2,3 : May 29, June 3, 2025}
\text{Image Formation and the Pinhole Camera}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
- Recap of Lec 1 - What is an Image?
- Introduction to Pinhole Camera Model
-
Perspective Projection
- Projection Matrix
- Intrinsic Parameter Matrix
- Extrinsic Parameter Matrix
- Challenges with Pinhole Camera
- Use of lenses
- Field of View
- Depth of Field
- Intro to capturing color
\( \text{Agenda of this Lecture:}\)
\text{Recap of Lecture 1}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
- Course Introduction
- What and Why is Computer Vision?
- Computer Vision at UB
- Modules covered in the course
- Course Logistics
- Course Structure
- Course Instructors
- Timings and Office Hours
- Introduction to Images
- What is an Image?
- What is a Pixel?
- Creating Images using Python code
\text{Recap of Lecture 1}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
- Course Introduction
- What and Why is Computer Vision?
- Computer Vision at UB
- Modules covered in the course
- Course Logistics
- Course Structure
- Course Instructors
- Timings and Office Hours
- Introduction to Images
- What is an Image?
- What is a Pixel?
- Creating Images using Python code
\( \text{Play with the}\)
\( \textbf{Live Code}\)
\( \text{on Course Website}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\( \text{Perspective Projection}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\( \text{Perspective Projection is easy!}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Magnification} = \frac{h}{H} = \frac{f}{Z}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\( \text{Let's Understand this with a Visualization}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Perspective Projection Properties}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Perspective Projection Properties}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Perspective Projection Properties}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Perspective Projection Properties}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\( \text{We need a mathematical model for Perspective Projection}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\begin{split}Z \begin{pmatrix}
\frac{fX}{Z} \\ \\
\frac{fY}{Z} \\ \\
1
\end{pmatrix}
=
\begin{pmatrix}
fX \\
fY \\
Z
\end{pmatrix} = \begin{bmatrix}
f & 0 & 0 & 0\\
0 & f & 0 & 0\\
0 & 0 & 1 & 0
\end{bmatrix}\begin{pmatrix}
X\\
Y\\
Z\\
1
\end{pmatrix}\end{split}
\begin{split}\begin{pmatrix}
fX + Zo_x \\
fY + Zo_y\\
Z
\end{pmatrix} = \begin{bmatrix}
f & 0 & o_x & 0\\
0 & f & o_y & 0\\
0 & 0 & 1 & 0
\end{bmatrix}\begin{pmatrix}
X\\
Y\\
Z\\
1
\end{pmatrix}\end{split}
\begin{split}K = \begin{bmatrix}
f_x & 0 & o_x \\
0 & f_y & o_y \\
0 & 0 & 1
\end{bmatrix}\end{split}
\( \text{Intrinsic Matrix}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\begin{split}s\begin{bmatrix}x\\
y\\
1
\end{bmatrix} = \begin{bmatrix}
f_x & 0 & o_x \\
0 & f_y & o_y \\
0 & 0 & 1
\end{bmatrix} \begin{bmatrix}
r_{11} & r_{12} & r_{13} & T_x \\
r_{21} & r_{22} & r_{23} & T_y \\
r_{31} & r_{32} & r_{33} & T_z
\end{bmatrix} \begin{bmatrix} X_w \\
Y_w \\
Z_w \\
1\end{bmatrix}\end{split}
\( \text{Perspective Projection}\)
\( \text{But how do I find Rotation and Translation Matrices?}\)
\text{Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\begin{split}s\begin{bmatrix}x\\
y\\
1
\end{bmatrix} = \begin{bmatrix}
f_x & 0 & o_x \\
0 & f_y & o_y \\
0 & 0 & 1
\end{bmatrix} \begin{bmatrix}
r_{11} & r_{12} & r_{13} & T_x \\
r_{21} & r_{22} & r_{23} & T_y \\
r_{31} & r_{32} & r_{33} & T_z
\end{bmatrix} \begin{bmatrix} X_w \\
Y_w \\
Z_w \\
1\end{bmatrix}\end{split}
\( \text{Perspective Projection}\)
\( \text{But how do I find Rotation and Translation Matrices?}\)
\( \textbf{Camera Calibration}\)
\text{Camera Calibration}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\( \text{What and How to perform Camera Calibration?}\)
Intro
\text{Camera Calibration}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Challenges with Perspective Projection}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
Too much time to capture an image with a small aperture size.
\text{Use of Lens for Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Use of Lens for Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Use of Lens for Image Formation}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
The process of Optical Zoom
\text{Properties arise while using lenses}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{Controlling DoF using aperture}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{The Exposure Triangle}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
\text{What about Color?}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
What does an Image consist of?
\text{What about Color?}
\text{Naresh Kumar Devulapally}
\text{CSE 4/573: CVIP, Summer 2025}
\text{May 29 2025}
TLDR: We have color sensors to capture color
We will revisit this towards the end of the course.