Briefly explain Image Representation in detail.
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A camera is a device that converts a $3 \mathrm{D}$ physical object into a $2 \mathrm{D}$ image of the object.

The depth information is lost, objects become inverted and scaled, and is analog in nature.

The 2D image is the output of the camera and is visual data.

The image is made of spatial coordinates $(x, y)$, and the value of the spatial coordinate represents the reflected light intensity or the brightness that spatial coordinate $(x, y)$.

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A computer cannot process the analog images or the raw images $i(x, y)$. It has to be converted to a digital image. The process of converting an analog image into its equivalent digital image is called digitization of images.

Digitization is a three-step process: sampling, quantization, and coding of images.

Digital Image $I(k, j)$ is defined as an analog image $ I (x, y)$ which is sampled to a spatial resolution of $(m \times n)$ pixels and quantized i.e. discretized both in spatial coordinates and in brightness.

A digital image is represented as a matrix of cells of width $\Delta x$ and height $\Delta y$. It is made up of a number of rows and columns, the size of the image being $(m \times n)$. Each row/column of the image is called a cell or a pixel.

The average light intensity over the picture element is given by,

$ I_0(k, j) \triangleq \frac{\int_0^{\Delta x} \int_0^{\Delta y} i[(k-1) \Delta x+x,(j-1) \Delta y+y] d y d x}{\Delta x \Delta y} $

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