Study Material

  UNIT 1: Image Representation and Modeling Q1: Explain the concept of digital image representation in detail. Answer : A digital image is a two-dimensional function that represents a physical object or scene. It is essentially a matrix where each element (pixel) contains intensity or color information. The size of the image is defined by its resolution (width × height), and each pixel has an intensity or color value. Pixel : The smallest unit of a digital image, typically represented as a square or rectangular cell. Each pixel has a value corresponding to its color or intensity. Resolution : Refers to the number of pixels in the image, which defines the level of detail. Higher resolution means more pixels and finer details. Color Models : Digital images can be grayscale (single intensity) or color (combining three channels for Red, Green, and Blue). Examples include RGB, CMYK, and YCbCr. Digital images are obtained by sampling and quantizing a continuous signal. S...

  Introduction to Data Compression Data Compression is the process of encoding information using fewer bits. It aims to reduce the size of the data while maintaining the necessary quality or information . Applications : Image, video, and audio compression (JPEG, MP3, video codecs). Goal : Reduce storage space and speed up transmission without losing essential information. 2. Data Compression vs Bandwidth Bandwidth refers to the data transmission capacity of a communication system (how much data can be transmitted per unit of time). Data Compression is a technique to reduce the size of data, leading to reduced transmission time, which increases effective bandwidth . Relation : Compressed data requires less bandwidth for transmission. Compression reduces storage and transmission costs , improving efficiency. Example: A 1MB image compressed to 100KB requires less bandwidth for transmission and storage. 3. Pixel Coding Pixel Coding involves ...

  Introduction to Image Restoration Image Restoration is the process of recovering an original image that has been degraded by known or unknown factors (such as blur, noise, or motion). It focuses on model-based correction , not just enhancing the image visually. Goal : Retrieve the most accurate version of the original image. 2. Image Formation Models The mathematical relationship between the original image, the degradation, and the observed image. General Model: g ( x , y ) = h ( x , y ) ∗ f ( x , y ) + η ( x , y ) g(x, y) = h(x, y) * f(x, y) + \eta(x, y) Where: g ( x , y ) g(x,y) g ( x , y ) = degraded image h ( x , y ) h(x,y) h ( x , y ) = degradation function (e.g., blur) f ( x , y ) f(x,y) f ( x , y ) = original image η ( x , y ) \eta(x,y) η ( x , y ) = noise ∗ * ∗ = convolution operation 3. Noise Models Describes how random variations corrupt an image. Common Noise Types: Gaussian Noise : Random values from a normal distribut...

  Introduction to Image Enhancement Image Enhancement refers to improving the visual appearance of an image or to convert the image to a form better suited for analysis by a human or machine. Goal: Highlight important features and suppress irrelevant details . Applied in areas like medical imaging , satellite imaging , robot vision , etc. 2. Point Operations Operations that modify each pixel independently without considering neighboring pixels. Types: Image Negative : Inverts the intensities to highlight hidden details. Log Transformation : Expands dark pixel values and compresses bright values. Power-Law (Gamma) Transformation : Controls overall brightness. Contrast Stretching : Increases dynamic range of pixel intensity. Thresholding : Converts image into binary by setting a threshold. Formula Example for Negative: s = L − 1 − r s = L - 1 - r Where: r r r = input pixel s s s = output pixel L L L = maximum intensity level (256 for 8...

  1. Sampling Theorem ▶ Theory: The Sampling Theorem , also known as the Nyquist-Shannon Sampling Theorem , is the foundation of digital signal and image processing. It states that a band-limited analog signal can be perfectly reconstructed from its samples if it is sampled at a frequency greater than or equal to twice the maximum frequency present in the signal. ▶ In image processing: Images are sampled in both horizontal and vertical directions. Insufficient sampling leads to loss of detail and aliasing .  2. Anti-Aliasing ▶ Theory: Aliasing is the effect of different signals becoming indistinguishable when sampled, leading to visual artifacts like moiré patterns. It occurs when the sampling rate is too low. Anti-aliasing techniques involve pre-filtering the image using a low-pass filter to remove high-frequency components before sampling. This ensures the sampled image retains important features without distortion.  3. Image Quantization ▶ Theory: Qu...