Image in Numbers

In computer science, a digital image is a discrete representation of a visual scene in the form of a matrix of numbers. Each element of this matrix corresponds to a pixel.

Mathematically, a grayscale image can be modeled by a matrix $ [M_{i,j}] $ where $ i $ and $ j $ denote the position of the pixel, and where the value $ M(i,j) $ represents its brightness.

The precision depends on the bit depth: with 8 bits, each pixel can take $ 2^8 = 256 $ values (from 0 to 255), while with 1 bit, each pixel can only take 2 values (black or white).

If the values are limited to a small set of integers (for example, from 0 to 9), the matrix can visually resemble ASCII art: the numbers become a simplified representation of the image.

Upload the image, indicate the number of digits, and click on convert.

Encoding an image digitally involves transforming each pixel into a numerical value representing its intensity.

In the case of a color image, each pixel has three components: Red (R), Green (G), and Blue (B). To obtain a grayscale value, the intensity is generally calculated using a weighted combination: $ L = 0.299R + 0.587G + 0.114B $ (this formula reflects the human eye's sensitivity to different colors).

Transforming numbers into an image involves performing the inverse operation: associating each number with a grayscale level.

If the numbers range from 0 to $ N-1 $, a linear correspondence can be defined: $ f(n) = \frac{255}{N-1} \times n $

Thus: $ 0 $ corresponds to black and $ N-1 $ to white; intermediate values produce proportional grayscale levels.

Each number is placed in its corresponding position in the matrix and then converted into a pixel.

If the image's width and height are unknown, line breaks can be used to determine the vertical dimension. Without this information, at least one of the two dimensions must be known to correctly reconstruct the image/picture.

Reducing the number of levels is equivalent to combining several real intensities into a single discrete value.

This operation introduces an error called quantization error.

The smaller $ N $ is, the greater the loss of information, which can cause visible effects such as posterization: the appearance of uniform areas instead of gradual gradients.