Vectors and Matrices: Small boldface letters (e.g., v) denote vectors; capital boldface letters (e.g., A) denote matrices. Vectors can be transposed (vα΅) to switch between row and column forms.
Complex Conjugation: The symbol * indicates complex conjugation, performed component-wise for vectors and matrices.
Hadamard Product and Division: Element-wise multiplication () and division ($/$) between vectors or matrices, applied element-by-element.
Image Function: Images are modeled as functions f(x) with domain Ξ© (spatial coordinates) and range in color space, possibly continuous or discrete, multi-dimensional (e.g., 2D, 3D+t).
Coordinate Transformations: Mapping between physical and normalized coordinates using scaling and offset parameters, enabling switching between image and real-world sizes.
Discrete vs. Continuous Images: Discrete images are represented on index sets (pixels/voxels), while continuous images are functions over real-valued domains.
1. In the context of mathematical notation in image processing, what does the symbol '*' represent when applied to vectors or matrices?
2. In the typical coordinate system used in image processing, where is the origin located and how are the axes oriented?
3. What is the primary role or purpose of discrete images in image processing?
Vectors β notation?
Bold lowercase letters, e.g., v.
Matrices β notation?
Bold uppercase letters, e.g., A.
Complex conjugation β symbol?
Asterisk (*).
Hadamard product β meaning?
Element-wise multiplication.
Image function β domain?
Spatial coordinates Ξ©.
Discrete images β representation?
Pixel grid as matrices or arrays.
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