Study Material

1. Sampling Theorem  Definition: The Sampling Theorem (Shannon-Nyquist) states that a continuous signal can be perfectly reconstructed from its samples if it is sampled at twice the maximum frequency present in the signal.  Formula: f s ≥ 2 f m a x f_s \geq 2f_{max} ​ where: f s f_s f s ​ = sampling frequency f m a x f_{max} f ma x ​ = highest frequency component in the signal  Application: Used in digitizing analog images to ensure no information is lost during sampling. 2. Anti-Aliasing Aliasing: Occurs when sampling is done below the Nyquist rate , leading to overlapping frequency components and distortion. Anti-Aliasing: A process to suppress high frequencies before sampling using low-pass filters to prevent aliasing. 3. Image Quantization  Definition: Process of mapping a range of continuous pixel values to a finite number of levels .  Types: Scalar Quantization : Each pixel is quantized independently. Vector Quantization : Blocks ...

  What is Image Processing? Image processing is a method to perform operations on an image to enhance it or extract useful information. It is a type of signal processing where the input is an image, and the output may be either an image or characteristics/features associated with that image. Goals of Image Processing Image Enhancement : Improving visual appearance (e.g., contrast, sharpness) Image Restoration : Removing noise or distortion Image Compression : Reducing the amount of data required to represent an image Feature Extraction : Identifying objects, edges, or patterns Image Analysis : Understanding and interpreting image content Object Recognition : Detecting and identifying objects in an image What is an Image? An image is a two-dimensional function f(x, y) , where x and y are spatial coordinates, and f is the intensity (brightness or color) at that point. For digital images, both x, y, and f are finite and discrete. Types of Image Representation...

 What should be the ideal size of the pixel? should it be big or small? The answer is given by the shannon nyquist theorem. As per this theorem, the sampling frequency should be greater than or equal to 2 ✕ fmax, where fmax is the highest frequency present in the image. SubSampling  The key idea in image sub-sampling is to throw away every other row and column to create a half-size image. When the sampling rate gets too low, we are not able to capture the details in the image anymore. Instead, we should have a minimum signal/image rate, called the Nyquist rate. Using Shannons Sampling Theorem, the minimum sampling should be such that : f s ≥ 2 f max

 Simple Image model  I(x, y, l) = σ(x, y, l) × L(l) Mach Bands Mach band effect is a phenomenon of lateral inhibition of rods and cones, where the sharp intensity changes are attenuated by the visual system. Components of Digital Camera The essential components of a digital camera are as follows A subsystem of sensors to capture the image. The subsystem uses photodiodes to convert light energy into electrical signals. A subsystem that converts analog signals to digital data. A storage subsystem for storing the captured images. A digital camera also has an immediate feedback system to see the captured image. Digital cameras can be connected to computers through a cable, to transfer images to the computer system.

  A digital imaging system is a set of devices for acquiring, storing, manipulating, and transmitting digital images. Components- Image Sensors Image Storage Image Processor Image Display Devices Networking Components Image Processing Software Human being perceive objects because of light. Light source are of two types- primary and secondary. The sun and Lamps are example of primary light sources. Nature of Light  wavelength - wavelength is the distance between two successive wave crests or wave troughs in the direction of travel. Amplitude - Amplitude is the maximum distance the oscillation travels, away from its horizontal axis. Frequency - The frequency of vibration is the number of waves crossing at a point.

Reflective Mode Imaging  Reflective mode imaging represents the simplest form of imaging and uses a sensor to acquire the digital image. All video cameras, digital cameras, and scanners use some types of sensors for capturing the image. Emissive Type Imaging  Emissive type imaging is the second type, where the images are acquired from self-luminous objects without the help of a radiation source. In emissive type imaging, the objects are self-luminous. The radiation emitted by the object is directly captured by the senor to form an image. Thermal Imaging is an example of emissive type imaging. Transmissive Imaging Transmissive imaging is the third type, where the radiation source illuminates the object. The absorption of radiation by the objects depends upon the nature of the material. Some of the radiation passes through the objects. The attenuated radiation is sensed into an image.

 Radiation Source  ↓                                                         ------ ------ --------------------------------------------------                                                       |                                             |                                                            |            ...