How to perform bilinear interpolation in Python

How to perform bilinear interpolation in Python

Bilinear interpolation is a method for interpolating values within a grid of known data points. It is commonly used in computer graphics and image processing to estimate pixel values between neighboring pixels. You can perform bilinear interpolation in Python using the following steps:

  1. Determine the four nearest data points to the target point.

  2. Calculate the distances between the target point and these four data points.

  3. Compute the weighted average of the values at the four data points, where the weights are inversely proportional to the distances.

Here's a Python function that performs bilinear interpolation:

def bilinear_interpolation(x, y, data):
    x1, y1 = int(x), int(y)
    x2, y2 = x1 + 1, y1 + 1

    # Check if the target point is at a data point
    if x1 == x2 or y1 == y2:
        return data[x1][y1]

    # Calculate distances
    dx1 = x2 - x
    dx2 = x - x1
    dy1 = y2 - y
    dy2 = y - y1

    # Perform bilinear interpolation
    value = (
        data[x1][y1] * dx1 * dy1 +
        data[x1][y2] * dx1 * dy2 +
        data[x2][y1] * dx2 * dy1 +
        data[x2][y2] * dx2 * dy2
    )

    return value

# Example usage:
data = [
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]

x = 1.5  # Target x-coordinate
y = 1.5  # Target y-coordinate

result = bilinear_interpolation(x, y, data)
print("Interpolated value:", result)

In this example:

  • bilinear_interpolation takes the target x and y coordinates and a 2D grid of data points.

  • It calculates the four nearest data points (x1, y1), (x1, y2), (x2, y1), and (x2, y2), where x1 and y1 are the floor values of x and y, and x2 and y2 are the ceiling values.

  • If the target point coincides with one of the data points, it returns the value at that data point.

  • Otherwise, it calculates the distances (dx1, dx2, dy1, dy2) and performs bilinear interpolation using the weighted average of the four data points.

In this example, the interpolated value at (1.5, 1.5) is calculated from the neighboring data points in the data grid. You can replace data, x, and y with your specific data and target coordinates for interpolation.

Examples

  1. How to perform bilinear interpolation in Python using NumPy?

    Description: This query seeks information on implementing bilinear interpolation in Python using the NumPy library.

    import numpy as np

def bilinear_interpolation(x, y, points):
    x0, y0, q11 = points[0]
    x1, y1, q21 = points[1]
    x2, y2, q12 = points[2]
    x3, y3, q22 = points[3]
    
    return (q11 * (x1 - x) * (y1 - y) +
            q21 * (x - x0) * (y1 - y) +
            q12 * (x1 - x) * (y - y0) +
            q22 * (x - x0) * (y - y0)) / ((x1 - x0) * (y1 - y0))

# Example usage
points = [(0, 0, 1), (1, 0, 2), (0, 1, 3), (1, 1, 4)]
result = bilinear_interpolation(0.5, 0.5, points)
print("Bilinear interpolation result:", result)

    Explanation: This code defines a function bilinear_interpolation() that performs bilinear interpolation given four points and coordinates (x, y). It then demonstrates how to use this function with example points and coordinates.

  2. How to implement bilinear interpolation in Python from scratch?

    Description: This query looks for a Python code example to implement bilinear interpolation without relying on external libraries.

    def bilinear_interpolation(x, y, points):
    x0, y0, q11 = points[0]
    x1, y1, q21 = points[1]
    x2, y2, q12 = points[2]
    x3, y3, q22 = points[3]
    
    return (q11 * (x1 - x) * (y1 - y) +
            q21 * (x - x0) * (y1 - y) +
            q12 * (x1 - x) * (y - y0) +
            q22 * (x - x0) * (y - y0)) / ((x1 - x0) * (y1 - y0))

# Example usage
points = [(0, 0, 1), (1, 0, 2), (0, 1, 3), (1, 1, 4)]
result = bilinear_interpolation(0.5, 0.5, points)
print("Bilinear interpolation result:", result)

    Explanation: This code provides a simple implementation of bilinear interpolation without using any external libraries, allowing users to understand the underlying calculations.

  3. How to perform bilinear interpolation in Python using SciPy?

    Description: This query seeks information on performing bilinear interpolation in Python using the SciPy library.

    from scipy.interpolate import griddata

points = [(0, 0, 1), (1, 0, 2), (0, 1, 3), (1, 1, 4)]
xi = [0.5]
yi = [0.5]

result = griddata((x, y), z, (xi, yi), method='linear')
print("Bilinear interpolation result:", result[0])

    Explanation: This code utilizes SciPy's griddata function to perform bilinear interpolation given the points and coordinates (x, y). It then demonstrates how to use this function to obtain the interpolated value.

  4. Performing bilinear interpolation in Python using OpenCV?

    Description: This query aims to understand how to perform bilinear interpolation in Python using the OpenCV library.

    import cv2

image = cv2.imread('image.jpg')
resized_image = cv2.resize(image, (new_width, new_height), interpolation=cv2.INTER_LINEAR)

    Explanation: This code snippet demonstrates how to use OpenCV's resize function with bilinear interpolation (cv2.INTER_LINEAR) to resize an image to a new width and height.

  5. How to perform bilinear interpolation for image resizing in Python?

    Description: This query seeks information on how to use bilinear interpolation for image resizing in Python.

    import cv2

image = cv2.imread('image.jpg')
resized_image = cv2.resize(image, (new_width, new_height), interpolation=cv2.INTER_LINEAR)

    Explanation: This code snippet demonstrates how to use the OpenCV library's resize function with bilinear interpolation (cv2.INTER_LINEAR) to resize an image to a new width and height.

  6. How to perform 2D bilinear interpolation in Python?

    Description: This query aims to understand how to perform bilinear interpolation in two dimensions in Python.

    from scipy.interpolate import interp2d

x = [0, 1]
y = [0, 1]
z = [[1, 2], [3, 4]]

f = interp2d(x, y, z, kind='linear')
result = f(0.5, 0.5)
print("Bilinear interpolation result:", result[0])

    Explanation: This code snippet utilizes SciPy's interp2d function to perform bilinear interpolation in two dimensions. It demonstrates how to use this function to obtain the interpolated value at a specific coordinate.

  7. Performing bilinear interpolation for 2D data in Python?

    Description: This query seeks guidance on performing bilinear interpolation for two-dimensional data in Python.

    from scipy.interpolate import interp2d

x = [0, 1]
y = [0, 1]
z = [[1, 2], [3, 4]]

f = interp2d(x, y, z, kind='linear')
result = f(0.5, 0.5)
print("Bilinear interpolation result:", result[0])

    Explanation: This code snippet demonstrates how to use SciPy's interp2d function to perform bilinear interpolation for 2D data, allowing users to obtain interpolated values at specified coordinates.

  8. How to perform bilinear interpolation for irregularly spaced data in Python?

    Description: This query looks for information on performing bilinear interpolation for irregularly spaced data in Python.

    from scipy.interpolate import griddata

points = [(0, 0, 1), (1, 0, 2), (0, 1, 3), (1, 1, 4)]
xi = [0.5]
yi = [0.5]

result = griddata((x, y), z, (xi, yi), method='linear')
print("Bilinear interpolation result:", result[0])

    Explanation: This code utilizes SciPy's griddata function to perform bilinear interpolation for irregularly spaced data, allowing users to obtain interpolated values at specified coordinates.

  9. How to perform bilinear interpolation on a grid in Python?

    Description: This query seeks guidance on performing bilinear interpolation on a grid of data in Python.

    from scipy.interpolate import griddata

points = [(0, 0, 1), (1, 0, 2), (0, 1, 3), (1, 1, 4)]
xi = [0.5]
yi = [0.5]

result = griddata((x, y), z, (xi, yi), method='linear')
print("Bilinear interpolation result:", result[0])

    Explanation: This code snippet demonstrates how to use SciPy's griddata function to perform bilinear interpolation on a grid of data, enabling users to obtain interpolated values at specified coordinates.

  10. How to perform bilinear interpolation for scattered data in Python?

    Description: This query aims to understand how to perform bilinear interpolation for scattered data in Python.

    from scipy.interpolate import griddata

points = [(0, 0, 1), (1, 0, 2), (0, 1, 3), (1, 1, 4)]
xi = [0.5]
yi = [0.5]

result = griddata((x, y), z, (xi, yi), method='linear')
print("Bilinear interpolation result:", result[0])

    Explanation: This code demonstrates how to use SciPy's griddata function to perform bilinear interpolation for scattered data, allowing users to obtain interpolated values at specified coordinates.

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