JNTU B.Tech III IMAGE PROCESSING Previous Question Paper (February - 2022 - R18)

The relationship between pixels in a digital image is defined by their spatial proximity and connectivity. The primary relationships are:

1. Neighbors of a pixel: A pixel at coordinates (x, y) has four horizontal and vertical neighbors, denoted as N4(p), with coordinates (x+1, y), (x-1, y), (x, y+1), and (x, y-1). The four diagonal neighbors, ND(p), are (x+1, y+1), (x+1, y-1), (x-1, y+1), and (x-1, y-1). Together, these form the eight neighbors, N8(p).
2. Adjacency: Two pixels are adjacent if they are connected. 4-adjacency occurs if q is in N4(p) and both have values from a set V. 8-adjacency occurs if q is in N8(p) and both have values from V. m-adjacency (mixed adjacency) is a modification of 8-adjacency that eliminates ambiguities in path connection by checking if the intersection of N4(p) and N4(q) contains no pixels from V.
3. Connectivity: Two pixels p and q are connected in a subset of pixels S if there exists a path between them consisting entirely of pixels in S.
4. Distance Measures: For pixels p(x, y), q(s, t), and z(u, v), a distance function D must satisfy non-negativity, symmetry, and triangle inequality. Common measures include:
   • Euclidean distance: D_e(p, q) = [(x-s)^2 + (y-t)^2]^(1/2)
   • City-block distance (D4): D_4(p, q) = |x-s| + |y-t|
   • Chessboard distance (D8): D_8(p, q) = max(|x-s|, |y-t|)

The 2D Discrete Cosine Transform (DCT) is a technique for converting spatial domain image data into the frequency domain, widely used in image compression standards like JPEG. Its key properties include:

1. Energy Compaction: The DCT exhibits high energy compaction, meaning that most of the signal information is concentrated in a few low-frequency coefficients in the top-left corner of the transform matrix. This allows for significant data reduction by discarding high-frequency coefficients.
2. Decorrelation: It effectively decorrelates the pixels of an image, transforming highly correlated spatial data into independent frequency components.
3. Separability: The 2D-DCT is separable, meaning a 2D transform can be computed by performing a 1D-DCT on the rows followed by a 1D-DCT on the columns (or vice versa). This reduces computational complexity from O(N^4) to O(N^2 log N).
4. Real-valued Transform: Unlike the Discrete Fourier Transform (DFT), the DCT uses only real numbers, avoiding complex arithmetic and phase information, which simplifies hardware and software implementation.
5. Symmetry: The basis functions of the DCT are cosine waves, which provide excellent approximation for signals with high correlation, such as natural images, and minimize boundary artifacts compared to the DFT.