An age old proven technique for image resizing

Why to read?

Anytime, was you curious to know how you are able to zoom small resolution picture to bigger size?

Bilinear interpolation is commonly used in image resizing, geometric transformations (such as rotation or scaling), and texture mapping in computer graphics. It allows for smooth transitions between pixel values and helps preserve image details and quality during resizing or transformation operations.

How it works

Bilinear interpolation is a method used to estimate values of a function or pixel intensities at positions that lie between known data points in a regular grid.

Understanding with example

To understand bilinear interpolation, let's consider a simple 2D case with a regular grid of data points. Suppose we have a square grid with four known data points at the corners: (x1, y1), (x1, y2), (x2, y1), and (x2, y2). Each data point has a corresponding value or intensity.

Bilinear interpolation aims to estimate the value at a position (x, y) within this grid, where (x1 <= x <= x2) and (y1 <= y <= y2). The estimated value is calculated by performing a weighted average of the surrounding known data points based on their distances from the target position.

The bilinear interpolation process involves the following steps:

1. Calculate Weights:
2. First, the distances between the target position (x, y) and the four known data points are computed. Let's denote these distances as dx1, dx2, dy1, and dy2. The weights for interpolation are then calculated as follows:
3. w1 = (x2 - x) * (y2 - y)
4. w2 = (x - x1) * (y2 - y)
5. w3 = (x2 - x) * (y - y1)
6. w4 = (x - x1) * (y - y1)
7. Weighted Average:
8. Next, the values or intensities of the known data points are multiplied by their corresponding weights. These weighted values are then summed together to obtain the interpolated value at the target position:
9. Interpolated value = w1 * Value1 + w2 * Value2 + w3 * Value3 + w4 * Value4

The interpolation weights are determined based on the relative distances of the target position to the four known data points. The closer a known data point is to the target position, the higher its weight in the interpolation.

Note

Bilinear interpolation assumes that the data between the known points changes linearly within the grid. While it may not capture complex variations accurately, it provides a smooth estimation that is visually pleasing and useful in many applications.

Thanks Note

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