Build a comprehensive image processing library implementing convolution filters, morphological operations, FFT, and image restoration from scratch.
Build a comprehensive image processing library implementing convolution filters, morphological operations, FFT, and image restoration from scratch. This comprehensive guide covers everything from design through implementation, testing, and deployment.
Convolution: (f * g)[x,y] = sum over (i,j) of f[i,j] × g[x-i, y-j]. Implement naive O(HW × kh × kw) algorithm and FFT-based O(HW log(HW)) algorithm for large kernels. Common kernels: Gaussian blur (smoothing), Sobel edge detection (horizontal/vertical gradients), Laplacian (edge sharpening), unsharp mask (enhancement). Implement correlation (no flip) and convolution (180° flip of kernel) — most image filters use correlation despite being called convolution.
10 components required for this project.
| # | Component | Purpose | Qty |
|---|---|---|---|
| 1 | Python 3.10+ | Library implementation | x1 |
| 2 | NumPy | Array operations (no OpenCV for core algos) | x1 |
| 3 | Pillow | Image loading and saving | x1 |
| 4 | Matplotlib | Visualization of processing results | x1 |
| 5 | scipy (FFT comparison) | Reference comparison | x1 |
| 6 | pytest | Testing with known filter outputs | x1 |
| 7 | OpenCV (reference only) | Validating results | x1 |
| 8 | Jupyter Notebook | Interactive visual exploration | x1 |
| 9 | ImageMagick | Additional reference implementation | x1 |
| 10 | Standard test images (Lena, Cameraman) | Classic image processing benchmarks | x1 |
Follow these 3 steps carefully.
Convolution: (f * g)[x,y] = sum over (i,j) of f[i,j] × g[x-i, y-j]. Implement naive O(HW × kh × kw) algorithm and FFT-based O(HW log(HW)) algorithm for large kernels. Common kernels: Gaussian blur (smoothing), Sobel edge detection (horizontal/vertical gradients), Laplacian (edge sharpening), unsharp mask (enhancement). Implement correlation (no flip) and convolution (180° flip of kernel) — most image filters use correlation despite being called convolution.
Binary morphology works on binary images using structuring elements (small binary kernels). Erosion: pixel=1 only if all structuring element pixels are 1. Dilation: pixel=1 if any structuring element pixel is 1. Opening = erosion → dilation (removes small objects, smooths boundaries). Closing = dilation → erosion (fills small holes, connects nearby objects). Skeletonization: repeatedly erode until single-pixel-wide skeleton. Hit-or-Miss transform for shape detection.
2D FFT converts image from spatial to frequency domain. Low frequencies (center): overall brightness, large-scale variations. High frequencies (edges, periphery): fine detail, edges, noise. Filtering in frequency domain: multiply FFT by filter mask, apply inverse FFT. Low-pass filter (Gaussian): retain low frequencies → smooth image. High-pass filter: retain high frequencies → edge detection. Band-pass: retain specific frequency band. Show frequency spectrum as log-magnitude image.
Core code for image_processor.py:
Test Image Processing Library by verifying each subsystem individually before full integration.
Verify power voltages, check ground connections, use serial monitor for debug.
An interactive simulator will be available here — simulate circuits and run code in-browser without hardware.