Image representation and pixel operations

Updated 07 Oct 2026

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Image and digital representation
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  Image capture -> depends on illumination, surfaces, optics, sensor response, and noise.
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  Image processing -> transforms image data.
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  Computer vision -> uses image data to infer scene properties.
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  Raster image
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    Pixels -> values arranged on a grid.
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    Sampling -> selects spatial locations.
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    Quantization -> maps measurements to finite values.
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    Spatial resolution -> number of sampled locations.
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    Bit depth -> number of representable levels.
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  Vector graphics -> describe shapes rather than a fixed pixel grid.
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  Color representations
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    RGB -> red, green, and blue channels.
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    Grayscale -> intensity values.
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    Binary image -> two values.
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    Indexed color -> palette indices.
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    Alpha -> opacity.
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  File encoding -> defines how image data is represented and compressed.
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    Lossy compression -> discards some information.
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  Physical print size -> not determined by pixel dimensions alone.
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Neighborhoods and operations
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  Connectivity
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    4-neighborhood -> horizontal and vertical neighbors.
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    8-neighborhood -> horizontal, vertical, and diagonal neighbors.
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    Connectivity choice affects region and edge interpretation.
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  Distance metrics
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    Euclidean -> $d_2=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$ .
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    Manhattan -> $d_1=|x_1-x_2|+|y_1-y_2|$ .
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    Chebyshev -> $d_\infty=\max(|x_1-x_2|,|y_1-y_2|)$ .
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  Cropping -> selects a region.
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  Resizing -> resamples pixels and requires interpolation.
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    Nearest-neighbor -> preserves labels.
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    Bilinear interpolation -> blends four samples
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    Bicubic interpolation -> uses a larger neighborhood and can overshoot.
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    Choose by data type: continuous values or class labels.
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Image representation and pixel operations

Image and digital representation

Neighborhoods and operations

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