INT345: COMPUTER VISION
UNIT-2
Lecture-1
Camera
• A camera captures light from a scene.
• It records an image using a sensor.
• The sensor can be digital or analog.
• Digital sensors include CMOS and CCD types.
• sensors use film for recording images.
• Cameras help in capturing visual scene details.
Camera
Camera Geometry
• A camera captures a real 3D scene.
• The image is converted into 2D format.
• This conversion leads to losing one dimension.
• Computer vision helps recover missing information.
• It provides a high-level image understanding.
• CV restores 3D details from 2D images.
Camera Models
• A camera model represents 3D to 2D projection.
• It helps in calibration, vision, and reconstruction.
• Models vary based on lens and projection methods.
• Different applications require specific camera models.
• Understanding models improves image processing tasks.
• Camera models are essential for accurate vision.
Types of Camera Models
✅ Pinhole model for basic image projection.
✅ Thin lens model for real-world photography.
✅ Affine model for flat imaging applications.
✅ Projective model for 3D reconstruction.
✅ Fish-eye model for wide-angle imaging.
✅ Omnidirectional model for robotics and self-driving cars.
Working of Camera
Comparison of Camera Models
Camera Model Lens? Depth Info? Used in Pros Cons
Needs high
Pinhole Model ❌ No ✅ Yes CV, AI No distortion
light
Thin Lens Autofocus,
✅ Yes ✅ Yes Photography Lens distortion
Model zoom
Satellites, Fast
Affine Model ✅ Yes ❌ No No perspective
scanners processing
Projective
✅ Yes ✅ Yes 3D vision, AI Realistic Complex math
Model
VR, 360°
Fish-Eye Model ✅ Yes ✅ Yes Ultra-wide view Image warping
cameras
Robotics, self- Complex
Omnidirectional ✅ Yes ✅ Yes 360° capture
driving cars calibration
Thank You
INT345: COMPUTER VISION
UNIT-2
Lecture-2
Pin Hole camera
• Simplest way to represent 3D scene into 2D image plane.
• It does not use any lenses
• It relies on a small aperture (pinhole)
• to allow light rays to pass through
• and form an inverted image on the opposite side.
Working Principle
• A pinhole camera consists of:
✅ A small hole (aperture) that lets light in.
✅ A light-tight box that prevents other light from entering.
✅ A screen or film where the image is projected.
Projection Mechanism
• Light from a 3D object passes through the pinhole.
• The image forms upside down on the image plane.
• The smaller the pinhole,
• the sharper the image
• but darker it becomes.
Pin Hole Camera
Pin Hole Camera
• we can see that a real world 3D object tree’s
• inverted 2D image is formed
• by using a pinhole camera model.
Pin Hole Camera working
Pin Hole Camera working
• f → distance between the image and the screen
• z → distance of the object from the screen
• (x, y, z) → real 3D world coordinates
• (u, v) → 2D image coordinates
Pin Hole Camera
• Ratio of both the triangles will be the same
• and will have the same angle
• Size of image (u, v) is directly proportional to f.
• So, bigger the focal length(f), bigger the image
• Size of image (u, v) is inversely proportional to z.
Thank You
INT345: COMPUTER VISION
UNIT-2
Lecture-3
Pinhole Camera Equation for Image
formation
Advantages
• ✔ No lens distortion (unlike lens-based cameras).
✔ Simple and cheap to construct.
✔ Large depth of field (everything appears in focus).
Disadvantages
• 🚫 Low brightness due to small aperture.
🚫 Requires long exposure time to capture images.
🚫 Limited sharpness because diffraction blurs details.
Example
Camera with lenses
• A camera with lenses is a real-world model
• where a lens system is used to focus light
• onto an image sensor.
• overcomes the limitations of a simple pinhole camera
• by allowing more light to enter
• while still maintaining sharp focus.
Camera with lenses
Thank You
INT345: COMPUTER VISION
UNIT-2
Lecture-4
Camera with lenses working
• Light from a 3D scene enters the camera lens.
• The lens focuses the light onto the image sensor
(CCD/CMOS).
• The sensor converts the light into an electronic image.
• The image is captured and stored digitally.
Camera with lenses equation
Types of Lenses in Cameras
• Convex Lens (Converging Lens)
• Concave Lens (Diverging Lens)
• Zoom Lens
• Wide-Angle Lens
Types of Lenses in Cameras
• Convex Lens (Converging Lens)
• Focuses light to a single point on the sensor.
• Used in most DSLRs, mobile cameras, webcams.
• Concave Lens (Diverging Lens)
• Spreads light out, reducing magnification.
• Used in wide-angle cameras and virtual reality lenses.
Types of Lenses in Cameras
• Zoom Lens
• Variable focal length, adjusts zoom level.
• Used in CCTV cameras, DSLR lenses.
• Wide-Angle Lens
• Captures a wider field of view.
• Used in sports, landscape photography.
Concave and Convex
Zoom lens
Wide lens
Thank You
INT345: COMPUTER VISION
UNIT-2
Lecture-5
CCD Cameras (Charge-Coupled Device
Cameras)
• It is a type of digital imaging device that
• converts light into electrical signals.
• These cameras are widely used in :
• astronomy, microscopy, medical imaging
• and industrial inspection
• due to their high sensitivity and low noise.
Working of CCD Cameras
• Light Capture
Photons from a scene hit the CCD sensor.
• Electron Generation
The sensor converts light into electrons.
• Charge Storage
Each pixel stores charge proportional to
light intensity.
• Charge Transfer
Charges move across the chip in a
controlled manner.
• Readout and Conversion
The charge is converted to a digital
Advantages of CCD Cameras
• High Image Quality
• High Sensitivity – Works well in low-light
conditions.
• Low Noise – Generates clearer images
• Uniform Pixel Response
• No variation in brightness or color across pixels.
• Good Dynamic Range
• Captures both bright and dark areas accurately.
Disadvantages of CCD Cameras
• High Power Consumption – Requires more power
than CMOS sensors.
• Expensive Manufacturing – More costly to
produce than CMOS cameras.
• Slower Readout Speed – Takes longer to capture
and process images.
• Blooming Effect – Excess charge can spill over
to neighboring pixels.
Lens distortion
• It is deviation from a perfect projection of a
scene
• due to imperfections in a camera lens.
• It causes straight lines in the real world to
appear:
• curved or misshaped in an image.
• This happens because
• different parts of the lens bend light unevenly.
Thank You
INT345: COMPUTER VISION
UNIT-2
Lecture-6
General Projective Cameras
• A projective camera models
• the perspective projection of a 3D scene
• onto a 2D image plane.
• It is described by the camera projection
matrix-
𝑃=𝐾[𝑅∣𝑡]
• (K) → Defines focal length, principal point,
and skew.
• ([R | t]) → Defines camera position and
orientation in 3D space.
General Projective Cameras
• Homogeneous Coordinates:
• 3D world points (X, Y, Z, 1) are mapped
• to 2D image points (x, y, 1) via projective
transformation.
• Given a 3D point: (X,Y,Z)=(10,5,20)
• The homogeneous form is: (10,5,20,1)
• Application:
• 3D vision, AR, robotics, mapping.
Intrinsic Parameters (K)
• It define internal characteristics of a camera
• that convert real-world distances into pixel
coordinates.
• It includes the
• focal length,
• principal point,
• and pixel scaling.
Extrinsic Parameters ([R | t])
• It describe position and orientation of camera
• in the world coordinate system.
• It consists of:
• Rotation Matrix (R) → Describes the camera’s orientation.
• Translation Vector (t) → Describes the camera’s position in
the world.
Extrinsic Parameters Example
Complete Projection Formula
Example
INT345: COMPUTER VISION
UNIT-2
Lecture-7
Affine Cameras
• It is a simplified version of a projective camera
• where perspective effects are ignored
• meaning that parallel lines in 3D remain parallel in 2D.
• It represents a 3D point (X,Y,Z)
• as a 2D image point (x,y) using the equation:
Affine Cameras
• Accurate when object is small and distant.
• Most useful for recognition.
Example
Key Properties & Application:
• No Perspective Distortion:
Parallel lines remain parallel after transformation.
• Linear Projection:
Preserves ratios and angles in small regions.
• Used in projection,
• planar motion tracking, and face alignment.
• Works well when the camera is far from the object.
Camera Calibration
• It is the process of estimating the intrinsic (K)
• and extrinsic parameters ([R | t]) to correct distortions
• It estimates the parameters of
• Lens, image sensor of an image or video.
• to correct for lens distortion,
• It used in machine vision to detect and measure objects.
• robotics, navigation systems, 3-D scene reconstruction.
Camera Calibration
Summary
Camera Type Projection Model Use Case
Pinhole Camera Perspective Projection 3D Reconstruction
Affine Camera Weak Perspective Object Recognition
Projective Camera Full Perspective Model AR/VR Applications
Fisheye Camera Wide-Angle Distorted Surveillance/VR
Thank You
INT345: COMPUTER VISION
UNIT-2
Lecture-8 (2-D Projective Geometry )
Projective Geometry
• It is used to describe how 2D points
• transform under perspective projection.
• It extends Euclidean geometry by
• introducing homogeneous coordinates,
• allowing for operations such as scaling,
• translation, rotation, and perspective transformation.
Planar Geometry & Projective Spaces
• Euclidean Geometry:
• regular 2D geometry
• where we represent a point as (x,y)
• .Projective Geometry:
• It extends Euclidean geometry
• by adding points at infinity,
• making it possible to handle perspective transformations.
Projective Geometry
Homogeneous coordinates
• simply add an extra dimension to the bottom of the vector
• with an entry of 1.
• We then multiply the entire new vector
• by an arbitrary scaling factor kp, like so:
Homogeneous coordinates
• To transform back to our original x, y representation,
• divide the first two vector entries by the third entry
• which is always equal to the scaling factor kp,
• and we arrive back at our original x and y terms.
Example
Homography
• A homography is a special matrix
• transforms one plane to another
• while preserving straight lines.
• It is represented as a 3×3 matrix
Homography
• It preserves collinearity and cross ratio
• collinearity (straight lines remain straight)
• cross-ratio (ratios of distances along a line remain
unchanged).
Homography
Homography
• (x,y,w) are the homogeneous coordinates
• (x′,y′,w′) are the transformed coordinates.
• H is the homography matrix.
• To convert back to Euclidean coordinates:
Properties of Homography
• A homography transformation:
• Maps straight lines to straight lines.
• Preserves collinearity
• (points that lie on a line remain on a line after transformation).
• Can handle perspective distortions
• (e.g., a tilted book page appearing rectangular).
• Needs at least 4 points to compute.
Example
Example
Example
Computing Homography from 4 Points
Applications of Homography
• Image Stitching (Panoramic Photos)
• Takes two overlapping images and aligns them.
• Used in Google Photos & Photoshop.
• Perspective Correction
• Used to correct tilted images, such as scanning documents.
Thank You
