Capture and representation are the foundational stages that transform a real-world scene into a digital image suitable for subsequent processing and analysis.

1. Image Capture

1.1 Physical Interaction and Illumination

• A scene comprises objects illuminated by natural or artificial light sources.

• Light reflected from or transmitted through the scene carries information about shape, color, and texture.

1.2 Optical System

• A lens focuses incoming light rays onto the image sensor.

• The aperture adjusts the light flux, trading off depth of field and brightness.

• The shutter controls exposure time, influencing motion blur and noise levels.

1.3 Sensor Technologies

• CCD (Charge-Coupled Device) and CMOS (Complementary Metal-Oxide Semiconductor) arrays consist of millions of photodiodes that convert photons into analog voltages1.

• Line-scan sensors capture one row at a time (common in scanners); area-scan sensors capture the full 2D scene at once.

1.4 Digitization: Sampling and Quantization

• Sampling discretizes the continuous spatial domain into an $M \times N$ grid of pixels (spatial resolution).

• Quantization maps each pixel’s analog voltage into a finite set of levels (gray-level or color resolution).

• E.g., an 8-bit grayscale image uses values 0–255 per pixel2.

• Higher spatial or gray-level resolution improves fidelity but increases data size and noise sensitivity.

2. Image Representation

2.1 Pixel-Based Models

• A digital image is a 2D function $I(u,v)$ where $u,v\in\{0,\dots,M-1\}\times\{0,\dots,N-1\}$ and

$$I(u,v)\in\{0,1,\dots,2^B-1\},$$

with $B$ = number of bits per pixel3.

• Grayscale: Single channel of intensities.

• RGB Color: Three channels—Red, Green, Blue—each quantized separately.

2.2 Data Structures and File Formats

• Bitmap (raster) stores raw pixel arrays (e.g., BMP, TIFF, PNG).

• Compressed formats exploit redundancy via lossless (PNG) or lossy (JPEG) schemes.

• Vector graphics (SVG) represent shapes mathematically—more suited to diagrams than natural images4.

2.3 Mathematical Models

• Pinhole Camera Model:

  $$x = f\,\frac{X}{Z},\quad y = f\,\frac{Y}{Z},$$

  where $(X,Y,Z)$ are world coordinates, $(x,y)$ image plane coordinates, and $f$ focal length.

• Lens Distortion: Real lenses introduce radial and tangential distortion functions that must be calibrated and corrected.

Understanding capture and representation is critical: it determines image fidelity, influences noise characteristics, and underpins all higher-level vision algorithms.