Interpolation Methods in Image Resizing

Image resizing is a fundamental operation in digital image processing, computer graphics, and computer vision. Whether you are a photographer preparing images for print, a web developer optimizing assets for faster load times, or a researcher analyzing satellite images, resizing is unavoidable. But resizing an image is not as simple as stretching a rubber band; digital images consist of discrete pixels, and when we change the size of an image, we must create new pixel values that did not exist in the original.

This process of estimating new pixel values is called interpolation. Interpolation methods determine how missing data between known samples should be estimated. In the context of images, they define how colors between original pixels are computed when scaling up or down.

This blog aims to provide an exploration of interpolation methods in image resizing. We will cover the mathematical foundations, algorithmic principles, practical use cases, visual comparisons, and implementation details across popular libraries.

By the end, you will not only understand what interpolation is, but also gain the knowledge to choose the right method for your project.

1. Fundamentals of Image Resizing

What Is Image Resizing?

Image resizing refers to the process of changing the dimensions of an image. Resizing can be:

Upscaling (enlargement): Increasing the resolution of an image.
Downscaling (reduction): Decreasing the resolution of an image.

When downscaling, information is often lost because multiple pixels are merged. When upscaling, new pixels need to be invented, which requires intelligent estimation.

Role of Interpolation in Resizing

Interpolation provides the rules for estimating new pixel values when resizing. Without interpolation, enlarging an image would simply duplicate pixels, resulting in blocky, jagged artifacts. With interpolation, the result can be smoother and more visually appealing.

2. Mathematical Foundation of Interpolation

Before diving into specific methods, let us explore the mathematics underpinning interpolation.

Sampling Theory

Digital images are sampled versions of continuous real-world scenes. According to the Nyquist-Shannon sampling theorem, to reconstruct a continuous signal without loss, it must be sampled at twice its highest frequency. However, images are often resampled at arbitrary scales, which requires interpolation.

Pixel Grids and Discrete Data

An image is essentially a 2D grid of values. Each pixel represents an intensity (grayscale) or a vector of intensities (RGB). When resizing, the new grid does not align perfectly with the old one, requiring approximation.

Continuous Approximation

Interpolation methods can be thought of as different ways of approximating the continuous underlying image function from discrete samples.

3. Categories of Interpolation Methods

Interpolation methods can be categorized into:

Nearest-Neighbor – simplest, fastest, but produces jagged edges.
Bilinear – smoother results, but can blur edges.
Bicubic – balances sharpness and smoothness.
Lanczos – high-quality method using sinc functions.
Spline-Based – mathematically smooth curves.
Advanced & Hybrid – edge-directed and AI-powered methods.

4. Nearest-Neighbor Interpolation

Algorithm Explained

Nearest-neighbor interpolation assigns each new pixel the value of the nearest original pixel. No averaging is done.

Mathematical Formula

For a target pixel at coordinate (x, y), we map it back to the source coordinates and pick the nearest integer location.

Advantages

Extremely fast.
No blurring; original pixel values preserved.

Disadvantages

Produces blocky, jagged artifacts.
Poor for photographic images.

Use Cases

Pixel art scaling.
Medical images where exact values matter.
Situations where speed outweighs quality.

5. Bilinear Interpolation

Core Concept

Bilinear interpolation uses the four nearest neighbors of a pixel and computes a weighted average based on distances.

Step-by-Step Computation

Identify four surrounding pixels.
Compute interpolation along x-axis.
Compute interpolation along y-axis.

Visual Characteristics

Smoother than nearest-neighbor.
Introduces slight blurring.

Performance

Slower than nearest-neighbor, but still efficient.
Widely used in real-time applications.

6. Bicubic Interpolation

Mathematical Details

Bicubic interpolation considers 16 neighboring pixels (4x4 area). It uses cubic polynomials to compute values.

Kernel Functions

Common bicubic kernels include Catmull-Rom and Mitchell-Netravali.

Edge Handling

Special boundary conditions needed near edges.

Comparison

Sharper than bilinear.
Higher computational cost.

7. Lanczos Interpolation

Concept of Sinc Function

Lanczos is based on the sinc function, the ideal interpolation kernel in signal processing.

Windowed Sinc Filtering

Since sinc is infinite, it is truncated using a Lanczos window (e.g., radius 2 or 3).

Variants

Lanczos-2: faster, less sharp.
Lanczos-3: slower, sharper, often preferred.

Applications

Professional photo editing.
Printing industry.

8. Spline-Based Interpolation

B-Splines

Smooth approximations that minimize error.

Cubic Splines

Piecewise cubic polynomials with continuity constraints.

Catmull-Rom Splines

Preserve shape of curves, often used in graphics.

Trade-Offs

Smooth but may overshoot.
More computationally expensive.

9. Advanced Interpolation Techniques

Edge-Directed Interpolation

Preserves edges better by adapting interpolation direction.

New Edge-Directed Interpolation (NEDI)

Uses covariance estimation for high-quality edge preservation.

Super-Resolution

Uses multiple images or deep learning to generate high-resolution details.

AI-Based Interpolation

Deep neural networks can hallucinate details, outperforming classical methods.

10. Comparative Analysis

Nearest-Neighbor: Fastest, worst quality.
Bilinear: Balance between speed and quality.
Bicubic: Preferred general-purpose method.
Lanczos: Best for high-quality enlargements.
Splines: Smooth, mathematically elegant.
AI: Highest quality, but resource-intensive.

Artifacts include blurring, ringing, and aliasing depending on the method.

11. Interpolation in Different Domains

Photography: Bicubic and Lanczos dominate.
Medical Imaging: Nearest-neighbor or spline for accuracy.
Satellite Imaging: Edge-preserving methods essential.
Computer Vision: Often use bilinear for efficiency.
Video Streaming: Lanczos or bicubic for downscaling.

12. Practical Guidelines

Use nearest-neighbor for pixel art.
Use bilinear for fast previews.
Use bicubic for general-purpose photography.
Use Lanczos for print and professional work.
Use AI methods when computational cost is acceptable.

13. Interpolation Methods used in Batch Image Resizer software

Name	Description
None	The pixels are not preserved during resize operation.
LeftTopToLeftTop	Left top point of the new image will coincide with the left top point of the original image. Crop will occur if required.
RightTopToRightTop	Right top point of the new image will coincide with the right top point of the original image. Crop will occur if required.
RightBottomToRightBottom	Right bottom point of the new image will coincide with the right bottom point of the original image. Crop will occur if required.
LeftBottomToLeftBottom	Left bottom point of the new image will coincide with the left bottom point of the original image. Crop will occur if required.
CenterToCenter	Center of the new image will coincide with the center of the original image. Crop will occur if required.
LanczosResample	Resample using lanczos algorithm with a=3.
NearestNeighbourResample	Resample using nearest neighbour algorithm.
AdaptiveResample	Resample using adaptive algorithm based on weighted and blended rational function and lanczos3 interpolation algorithms.
BilinearResample	Resample using bilinear interpolation. Image pre-filtering is allowed to remove the noice before resample, when needed
HighQualityResample	The high quality resample
CatmullRom	The Catmull-Rom cubic interpolation method.
CubicConvolution	The Cubic Convolution interpolation method
CubicBSpline	The CubicBSpline cubic interpolation method
Mitchell	The Mitchell cubic interpolation method
SinC	The Sinc (Lanczos3) cubic interpolation method
Bell	The Bell interpolation method

14. Conclusion

Interpolation is at the heart of image resizing. The method you choose affects sharpness, smoothness, and artifacts. From the simplicity of nearest-neighbor to the sophistication of deep learning, interpolation continues to evolve.

For practical work:

Use bicubic or Lanczos for quality.
Use bilinear for speed.
Explore AI for cutting-edge applications.

Ngoc Thanh