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This page contains information on Fourier, an open-source image processing and analysis library.
Fourier consists of several toolboxes that implement operations such as image I/O, geometric transformations, color space conversions, noise removal, smoothing, enhancement, morphology, edge detection, thresholding, segmentation, and visual (shape, color, texture) feature extraction.
Prominent features of Fourier include:
- Portability (written in strict ANSI C)
- Efficiency (optimized for speed without sacrificing from clarity or deviating from the ANSI standard)
- Flexibility (two modes of pixel access: linear and multidimensional)
- Adaptability (easy to isolate a particular function and use it in other software)
- Robustness (run-time checks for validating objects to reduce crashes due to programmer errors)
- Thread-safe error-handling (two modes, one for novices and the other for advanced users)
- Extensive documentation with Doxygen (references to the relevant literature)
The Beta version (v0.8) is available at Sourceforge.

Existing (E), Implemented (I), and Planned (P) functionality include

Category	Method	Status
Image I/O
	PNM (PBM, PGM, PPM) format	E
	BMP format	E
	JPEG format	E
	TIFF format	P
Geometric Transformations	Scaling	E
Geometric Transformations	Rotation	E
Arithmetic & Logic Operations	Add, Subtract, Multiply, Divide	E
Arithmetic & Logic Operations	Union, Intersection	E
Color Space Conversions
	RGB to HSV & HSV to RGB	E
	RGB to HSL & HSL to RGB	E
	RGB to HSI { standard, Kender } & HSI to RGB	E
	RGB to l1l2l3	E
	RGB to rgb	E
	RGB to OHTA (I1I2I3) & OHTA to RGB	E
	RGB to SCT & SCT to RGB	E
	RGB to CIE-Lab & CIE-Lab to RGB	E
	RGB to CIE-Luv & CIE-Luv to RGB	E
	CIE-Lab to LCH & LCH to CIE-Lab	E
	RGB to KL	P
	Trilinear interpolation { standard, caching }	I
	Prism interpolation { standard, caching }	I
	Pyramidal interpolation { standard, caching }	I
	Tetrahedral interpolation { standard, caching }	I
Grayscale Image Smoothing & Noise Removal	Add noise { Gaussian, Salt & Pepper, Speckle }	E
	Calculate Error Measures { MAE, MSE, RMSE, PSNR, NMSE }	E
	Mean filter	E
	Gaussian filter	E
	Fast Anisotropic Gaussian filter	E
	Classical Median filter	E
	Huang's Running Median filter	E
	Kopp's 3x3 Median filter	E
	Constant-Time Median filter	E
	Separable Median filter	E
	LUM filter	E
	Adaptive Smoothing filter	E
	Lee's Local Statistics filter	E
	Sigma filter	E
	Symmetric Nearest Neighbor filter	E
	Gradient Inverse Weighted Smoothing filter	E
	Kuwahara filter	E
	SUSAN filter	E
	Bilateral filter	E
	Local Contrast Entropy filter	E
	MLV filter	E
	MCV filter	E
	Adaptive MAD-based filter	E
	SDROM filter	E
	Perona-Malik Anisotropic Diffusion filter	E
	Robust Anisotropic Diffusion filter	E
	Modified Peak-and-Valley filter	E
	Hybrid Median filter	I
	Truncated Median filter	I
	Savitzky-Golay filter	I
	Meanshift filter	P
Grayscale Image Enhancement	Histogram Smoothing { Local, Gaussian }	E
	Histogram Matching	E
	Histogram Expansion	E
	Histogram Equalization	E
	Histogram Hyperbolization	E
	CCV Enhance	E
	Fuzzy Histogram Hyperbolization	I
	Retinex Enhancement	P
	Contrast Limited Adaptive Histogram Equalization	I
Binary and Grayscale Mathematical Morphology	Dilation	E
	Erosion	E
	Opening	E
	Closing	E
	Opening Top-Hat	E
	Closing Top-Hat (Bottom-Hat)	E
	Conditional Dilation	E
	Conditional Erosion	E
	Morphological Gradient	E
	Inf-Reconstruction	E
	Sup-Reconstruction	E
	Opening by Reconstruction	E
	Closing by Reconstruction	E
	Open-by-Reconstruction Top-Hat	E
	Close-by-Reconstruction Top-Hat	E
	H-minima Transform	E
	H-maxima Transform	E
	Regional minima	E
	Regional maxima	E
	Extended-minima Transform	E
	Extended-maxima Transform	E
	Alternating Sequential Filter	E
	Hole Filling	E
	Border Clearing	E
Thresholding	Otsu's method	E
	Kapur-Sahoo-Wong (Maximum Entropy) method	E
	Shanbhag's Fuzzy Entropy method	E
	Moment-Preserving method	E
	Renyi's Entropy method	E
	Ridler-Calvard (Iterative Selection) method	E
	Yen's method	E
	Li's Minimum Cross Entropy method	E
	Huang's Fuzzy Entropy method	E
	Bernsen's method	E
	Niblack's method	E
	Sauvola's method	E
	Savakis's method { standard, optimized }	E
	Recursive Otsu method	I
	Kittler-Illingworth (Minimum Error) method	I
	Lloyd's method	I
	Unimodal Thresholding	P
Grayscale Edge Detection	Roberts	E
	Prewitt	E
	Sobel	E
	Laplacian of Gaussian (LoG)	E
	Canny	E
	Deriche	E
	Shen-Castan (ISEF)	P
	SUSAN	P
Binary Image Processing	Connected Component Labeling (Blob Coloring) { union-find, hybrid, contour tracing }	E
	Majority Filter	E
	Region Filling	E
	Contour Tracing	E
	Pseudo Coloring	E
	Distance Transform	I
	Thinning	P
Shape Feature Extraction	Convex Hull (using Graham scan algorithm)	E
	Flusser's Affine Invariant Moments	E
	Aspect Ratio	E
	Chord Length Statistics {mean, variance, skewness, kurtosis }	E
	Circularity	E
	Compactness	E
	Contour Sequence Moments	E
	Ellipse-Related Features { major/minor axis length, aspect ratio, eccentricity, orientation }	E
	Ellipticity	E
	Elliptic Variance	E
	Equivalent Diameter	E
	Generic Fourier Descriptor	E
	Hu's Invariant Moments	E
	Maximum Diameter	E
	Area (using Bit-Quads)	E
	Centroid (center of mass)	E
	Radial Distance Measures { mean, stdev, entropy, roughness }	E
	Rectangularity	E
	Solidity	E
	Triangularity	E
	Zernike Moments	E
	Perimeter	I
	Asymmetry	I
	Pattern Spectrum	I
	Fourier Descriptor	I
	Chebyshev { Tchebichef } Moments	I
	Convex Hull (Melkman's algorithm)	P
	Edge Direction Histogram	P
Color Feature Extraction	Color Histogram	I
	Color Moments	I
	Color Coherence Vector (CCV)	I
	Color Correlogram	P
Texture Feature Extraction	Gray-Level Co-Occurrence Matrix Features (GLCM)	I
	Grey-Tone Difference Matrix Features	I
	Law's Texture Measures	P
	Gabor Texture Features	P
Color Image Segmentation	Statistical Region Merging (SRM)	E
	Efficient Graph-Based Image Segmentation	E
	Region-Based Segmentation in the HSI Color Space	I
	Mean-Shift Clustering	P
	Color Connected Component Labeling	I
Color Image Quantization	Wan's variance-based method	E
	Wu's method	E
	NeuQuant method	E
	K-means clustering method	I
Color Image Smoothing & Noise Removal	Adaptive Basic Vector Directional Filter	E
	Adaptive Center-Weighted Vector Directional Filter	E
	Adaptive Center-Weighted Directional-Distance Filter	E
	Adaptive Center-Weighted Vector Median Filter	E
	Adaptive Hybrid Directional Filter	E
	Adaptive Multichannel Non-Parametric Filter with Exponential Kernel	E
	Adaptive Multichannel Non-Parametric Filter with Gaussian Kernel	E
	Adaptive Nearest Neighbor Filter	E
	Adaptive Nearest Neighbor Multichannel Filter	E
	Adaptive Sigma Basic Vector Directional Filter based on Mean	E
	Adaptive Sigma Basic Vector Directional Filter based on Rank	E
	Adaptive Sigma Directional Distance Filter based on Mean	E
	Adaptive Sigma Directional Distance Filter based on Rank	E
	Adaptive Sigma Vector Median Filter based on Mean	E
	Adaptive Sigma Vector Median Filter based on Rank	E
	Alpha-Trimmed Vector Median Filter	E
	Adaptive Vector Median Filter	E
	Basic Vector Directional Filter	E
	Content-Based Rank Filter	E
	Combined Fuzzy Metric Filter	E
	Directional Distance Filter	E
	Entropy Basic Vector Directional Filter	E
	Entropy Directional Distance Filter	E
	Entropy Vector Median Filter	E
	Extended Vector Median Filter	E
	Fuzzy Vector Directional-Rational Hybrid Filter	E
	Fast Fuzzy Noise Reduction Filter	E
	Fast Modified Vector Median Filter	E
	Fuzzy Metric Vector Directional Filter	E
	Fuzzy Metric Directional Distance Filter	E
	Fuzzy Ordered Vector Directional Filter	E
	Fuzzy Ordered Vector Median Filter	E
	Fast Peer Group Filter	E
	Fuzzy Vector Directional Filter	E
	Fuzzy Vector Directional-Rational Hybrid Filter	E
	Fuzzy Vector Median Filter	E
	Fuzzy Vector Median-Rational Hybrid Filter	E
	Generalized Vector Directional Filter	E
	Hybrid Directional Filter	E
	Kernel Vector Median Filter	E
	Marginal Median Filter	E
	Modified Center-Weighted Vector Median Filter	E
	Peer Group Filter	E
	Peer Group Vector Median Filter	I
	Pairwise Vector Ordering Filter	E
	Rank-Ordered Differences Statistic Based Vector Median Filter	E
	Sigma Basic Vector Directional Filter based on Mean	E
	Sigma Basic Vector Directional Filter based on Rank	E
	Sigma Directional Distance Filter based on Mean	E
	Sigma Directional Distance Filter based on Rank	E
	Sigma Vector Median Filter based on Mean	E
	Sigma Vector Median Filter based on Rank	E
	Vector Median Filter	E
	Vector Median-Rational Hybrid Filter	E
	Vector Signal-Dependent Rank Order Mean Filter	E

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Last updated: 07/05/2008