Algorithms

SLIP includes algorithms which may be used for image processing. They are split into several categories:

Common algorithms:

Arithmetic Operations between ranges algorithms

• addition - masked addition - predicated addition
• subtraction - masked subtraction - predicated subtraction
• multiplication - masked multiplication - predicated multiplication
• division - masked division - predicated division
• negation - masked negation - predicated negation
• minimum - masked minimum - predicated minimum
• maximum - masked maximum - predicated maximum
• scalar addition - masked scalar addition - predicated scalar addition
• scalar subtraction - masked scalar subtraction - predicated scalar subtraction
• scalar multiplication - masked scalar multiplication - predicated scalar multiplication
• scalar division - masked scalar division - predicated scalar division
• iota - masked iota

Comparison-Distances between ranges algorithms

• generic distance map - masked generic distance map - predicated generic distance map
• generic distance - masked generic distance - predicated generic distance
• mean square difference - masked mean square difference - predicated mean square difference
• mean absolute difference - masked mean absolute difference - predicated mean absolute difference
• signal to noise ratio - masked signal to noise ratio - predicated signal to noise ratio
• decibel signal to noise ratio - masked decibel signal to noise ratio - predicated decibel signal to noise ratio
• peak signal to noise ratio - peak masked signal to noise ratio - predicated peak signal to noise ratio
• L2 squared distance - masked L2 squared distance - predicated L2 squared distance
• L2 distance - masked L2 distance - predicated L2 distance
• L1 distance - masked L1 distance - predicated L1 distance
• Linfinity distance - masked Linfinity distance - predicated Linfinity distance
• Minkowski distance - masked Minkowski distance - predicated Minkowski distance
• KullbackLeibler distance - masked KullbackLeibler distance - predicated KullbackLeibler distance
• Chi2 distance - masked Chi2 distance - predicated Chi2 distance
• Sructural SIMilarity (SSIM) - masked Sructural SIMilarity (SSIM) - predicated Sructural SIMilarity (SSIM)

Some comparison and distance functors:

• L1 distance
• L2 (Euclidean) distance
• L2 squared distance
• L1 relative error
• L2 relative error
• L2 squared relative error
• L1 distance between 2 vectors
• L2 distance between 2 vectors
• L2 squared distance between 2 vectors
• (optical flow) angular error in degree
• (optical flow) angular error in radian

Norms of a range algorithms

• squared L22 norm (squared Euclidean norm) - masked squared L2 (squared Euclidean norm) norm - predicated squared L2 (squared Euclidean norm) norm
• L2 norm (Euclidean norm) - masked L2 (Euclidean norm) norm - predicated L2 (Euclidean norm) norm
• L1 norm - masked L1 norm - predicated L1 norm

• Linfinity norm (Euclidean norm) - masked Linfinity norm - predicated Linfinity norm

Algorithms to change the dynamic of a range (affine, normal or sigmoid)

• general dynamic change - masked general dynamic change - predicated general dynamic change
• change dynamic to [0,1]

STL algorithms and numeric extensions

• copy algorithm optimized for slip iterators
• unary masked transform - unary predicated transform
• binary masked transform - binary predicated transform
• masqued max element - predicated masqued element
• masqued min element - predicated masqued element
• masqued generalized max element - predicated generalized masqued element
• masqued generalized min element - predicated generalized masqued element
• masked inner product - predicated inner product
• masked generalized inner product - predicated generalized inner product

Correlation algorithms

• standard crosscorrelation - masked standard crosscorrelation - predicated standard crosscorrelation
• normalized crosscorrelation - masked normalized crosscorrelation - predicated normalized crosscorrelation
• centered crosscorrelation - masked centered crosscorrelation - predicated centered crosscorrelation
• pseudo-normalized crosscorrelation - masked pseudo-normalized crosscorrelation - predicated pseudo-normalized crosscorrelation
• FFT standard crosscorrelation - complex FFT standard crosscorrelation - FFT circular crosscorrelation - FFT central part of the crosscorrelation
• FFT2d standard crosscorrelation - FFT2d circular crosscorrelation - FFT2d central part of the crosscorrelation
• FFT3d standard crosscorrelation - FFT3d circular crosscorrelation - FFT3d central part of the crosscorrelation
• crosscorrelation map between two 2d ranges
• autocorrelation - full autocorrelation - biased autocorrelation - unbiased autocorrelation
• biased autocorrelation matrix
• autocovariance - biased autocovariance - unbiased autocovariance
• biased autocovariance matrix

Statistics:

• cardinal - masked cardinal - predicated cardinal
• mean - masked mean - predicated mean
• recursive mean
• weighted mean
• standard deviation - masked standard deviation - predicated standard deviation
• unbiased standard deviation - masked unbiased standard deviation - predicated unbiased standard deviation
• variance - masked variance - predicated variance
• unbiased variance - masked unbiased variance - predicated unbiased variance
• recursive variance
• covariance - masked covariance - predicated covariance
• unbiased covariance - masked unbiased covariance - predicated unbiased covariance
• kurtosis - masked kurtosis - predicated kurtosis
• unbiased kurtosis - masked unbiased kurtosis - predicated unbiased kurtosis
• skewness - masked skewness - predicated skewness
• unbiased skewness - masked unbiased skewness - predicated unbiased skewness
• rms - masked rms - predicated rms
• median - masked median - predicated median
• median for a range of size n
• generalized median
• generalized median for a range of size n
• first quartile - masked first quartile - predicated first quartile
• third quartile - masked third quartile - predicated third quartile
• all statistics - masked all statistics - predicated all statistics
• all unbiased statistics - masked all unbiased statistics - predicated all unbiased statistics
• nth_moment - masked nth_moment - predicated nth_moment
• n max elements
• n min elements
• center - masked center - predicated center
• studentize - masked studentize - predicated studentize
• discrete histogram - masked discrete histogram - predicated discrete histogram
• real histogram
• cumulative histogram
• Principal Component Analysis (PCA) data reduction

Linear Algebra:

Common linear Algebra algorithms (algeabric operations, LU solve and inverse algorithms, householder Givens transforms...)

• aXpY operation
• complex L2 norm
• row matrix norm
• column matrix norm
• Frobenius matrix norm
• vector by scalar multiplication
• conjugate vector by scalar multiplication
• matrix by scalar multiplication
• hermitian left multiplication
• transpose left multiplication
• hermitian left matrix multiplication
• hermitian matrix vector multiplication
• matrix vector multiplication
• matrix matrix multiplication
• generalized matrix vector multiplication
• generalized matrix matrix multiplication
• matrix shift
• rank one update
• reduction
• complex and real inner product
• generalized inner product
• Rayleigh coefficient
• outer product
• rank1 x rank1 tensorial product
• rank1 x rank1 x rank1 tensorial product
• matrix transposition
• hermitian matrix transposition
• matrix determinant
• conjugate matrix
• real matrix
• imaginary matrix
• fill diagonal
• set diagonal
• get diagonal
• is real
• is complex
• epsilon value of a real or a complex

Linear algebra tests

• is real
• is complex
• is squared
• is hermitian
• is skew hermitian
• is symmetric
• is band matrix
• is triangular
• is upper bidiagonal
• is lower bidiagonal
• is upper hessenberg
• is lower hessenberg
• is upper triangular
• is lower triangular
• is null diagonal
• analyse matrix

Orthogonal transform algorithms

• Givens sinus and cosinus
• Right givens rotation multiplication
• Left givens rotation multiplication
• Complex right givens rotation multiplication
• Complex left givens rotation multiplication
• Householder vector
• Right householder update
• Left householder update
• Householder Hessenberg reduction of the square matrix

least square algorithms

• SVD linear least square with individual deviations
• SVD linear least square
• Multidimensional SVD linear least square with individual deviations
• Multidimensional SVD linear least square

Gram-Schmidt orthogonalisation algorithms

• Gram-Schmidt orthogonalization algorithm
• Gram-Schmidt orthogonormalization algorithm
• Modified Gram-Schmidt orthogonalization algorithm
• Modified Gram-Schmidt orthogonormalization algorithm
• Gram matrix computation

Linear algebra solve algorithms

• partial pivot
• lu solve
• lu decomposition
• tridiagonal lu decomposition
• Thomas (tridiagonal) solve
• Cholesky decomposition
• Cholesky solve
• tridiagonal cholesky decomposition
• Tridiagonal cholesky solve
• Diagonal solve
• Upper bidiagonal solve
• Lower bidiagonal solve
• Unit upper bidiagonal solve
• Unit lower bidiagonal solve
• upper triangular solve
• lower triangular solve
• Unit upper triangular solve
• Unit lower triangular solve
• Gauss solve
• Singular Value Decomposition solve
• Sylvester solve

Linear algebra inversion algorithms

• Matrix inversion
• LU inversion
• Cholesky inversion
• Upper triangular inversion
• Lower triangular inversion
• upper bidiagonal inversion
• lower bidiagonal inversion
• Thomas (tridiagonal) inversion
• Tridiagonal Cholesky inversion
• Pseudo inverse

Linear algebra eigen values algorithms

• Balance matrix
• Eigen values of a non hermitian matrix
• Eigen values and eigen vectors of a hermitian semi-definite positive matrix
• Spectral radius
• Schur decomposition
• QR Householder decomposition
• Bidiagonal reduction
• Singular Value Decomposition (SVD)
• Singular Value Decomposition (SVD) approximation

Signal and image processing

Fast Fourier Transform (FFT)

• Complex FFT
• Real FFT
• Inverse FFT
• FFT shift
• Complex FFT2d
• Real FFT2d
• Inverse FFT2d
• FFT2d shift
• Real FFT3d
• Inverse FFT3d
• FFT3d shift
• Discrete Cosinus Transform (DCT II)
• inverse Discrete Cosinus Transform (DCT III)

Convolution algorithms

• Full convolution - valid convolution - same convolution - FFT convolution - FFT circular convolution
• Full convolution2d - valid convolution 2d - same convolution 2d - FFT convolution 2d
• separable convolution 2d - FFT separable convolution 2d
• valid convolution 3d
• 3d fft convolution - 3d fft same convolution
• 3d separable convolution - 3d fft separable convolution

Noise generation algorithms

• Gaussian noise generation - masked Gaussian noise generation - predicated Gaussian noise generation
• Speckle noise generation - masked speckle noise generation - predicated speckle noise generation
• Uniform noise generation - masked uniform noise generation - predicated uniform noise generation
• Salt and pepper noise generation - masked Salt and pepper noise generation - predicated Salt and pepper noise generation

Interpolation algorithms

Bspline interpolation

• Bspline poles computation
• BSpline 1d interpolation coefficients computation
• BSpline 1d interpolation
• BSpline 2d interpolation coefficients computation
• BSpline 2d interpolation
• BSpline 3d interpolation coefficients computation
• BSpline 3d interpolation

Geometric transformations

• Bspline 1d resampling
• Bspline 2d resampling
• Bspline 3d resampling
• Bspline 2d rotation

Thresholding algorithms

• Simple threshold
• Double threshold
• Multiple threshold

Binarization algorithms

• binarization

Border treatment algorithms

• add borders to a 1d, 2d, 3d or 4d range
• add borders to a 1d container
• add borders to a 2d container
• add borders to a 3d container
• add borders to a 4d container
• fill borders of a 1d, 2d, 3d or 4d range
• update borders of a 1d, 2d, 3d or 4d range

Color space conversion functors

• RGB to luminance
• RGB to XYZ
• XYZ to RGB
• RGB to YCbCr
• YCbCr to RGB
• RGB to Cie Lab
• CieLab to RGB
• RGB to HSV
• HSV to RGB
• RGB to HSI
• HSV to RGB
• RGB to HSI (values between [0.0,1.0])
• HSV to RGB (values between [0.0,1.0])

Mathematics:

General constants and mathematics algorithms

• generic power function
• generic nth power
• functor returning the real part of real or complex
• functor returning the imaginary part of real or complex
• functor returning the absolute value of real or complex
• functor returning true if the first element is less than second one according to their absolute value
• functor returning true if the first element is greater than second one according to their absolute value
• functor that returns the std::min(x,y)
• functor that returns the std::max(x,y)
• functor that returns the sign(x)
• functor that returns the complex sign of a complex

• computes 2d Euclidean norm without destructive underflow or overflow

• slip mathematical constants

apply C functions to ranges

• Apply a C unary function to range - masked unary apply - predicated unary apply

finite difference algorithms

• finite differences kernels for derivation based on Taylor series
• finite differences derivatives of a 1d range
• finite differences derivatives of a 2d range
• finite differences derivatives of a 3d range
• finite differences derivatives of a 4d range
• apply a differential operator to a range
• apply 2 differential operators to a range
• apply 3 differential operators to a range

Differential operators functors

• x first derivative 2nd order central difference
• y first derivative 2nd order central difference
• z first derivative 2nd order central difference
• t first derivative 2nd order central difference
• x second derivative 2nd order central difference
• y second derivative 2nd order central difference
• xy second derivative 2nd order central difference
• Weicket xy second derivative 2nd order central difference
• xz second derivative 2nd order central difference
• yz second derivative 2nd order central difference
• z second derivative 2nd order central difference
• t second derivative 2nd order central difference
• Sapiro second derivative in the gradient direction (Iee) approximation
• Lucido second derivative in the gradient direction (Iee) approximation
• Augereau second derivative in the gradient direction (Iee) approximation
• Alvarez second derivative in the gradient direction (Iee) approximation
• Other Alvarez second derivative in the gradient direction (Iee) approximation
• Cohignac second derivative in the gradient dire (Iee) approximation
• Sapiro second derivative in the direction perpendicular to the gradient direction (Inn) approximation
• Lucido second derivative in the direction perpendicular to the gradient (Inn) approximation
• Augereau second derivative in the gradient direction perpendicular to the gradient (Inn) approximation
• Alvarez second derivative in the direction perpendicular to the gradient (Inn) approximation
• Other Alvarez second derivative in the direction perpendicular to the gradient (Inn) approximation
• Cohignac second derivative in the direction perpendicular to the gradient (Inn) approximation
• second derivative approximation according to a direction
• x first derivative first order Forward difference
• y first derivative first order Forward difference
• z first derivative first order Forward difference
• t first derivative first order Forward difference
• x first derivative first order Backward difference
• y first derivative first order Backward difference
• z first derivative first order Backward difference
• t first derivative first order Backward difference
• x Prewitt first derivative
• y Prewitt first derivative
• z Prewitt first derivative
• x Sobel first derivative
• y Sobel first derivative
• z Sobel first derivative
• 2nd order First directional derivative
• 2nd order Euclidean gradient norm
• 2nd order divergence
• 2nd order laplacian
• 2nd order 2-, 8-laplacian
• 2nd order 2d Lindeberg laplacian
• Osher and Sethian first order gradient norm approximation when sign(Iee) < 0
• Osher and Sethian first order gradient norm approximation when sign(Iee) > 0
• Brockett and Maragos first order gradient norm approximation when sign(Iee) < 0
• Brockett and Maragos first order gradient norm approximation when sign(Iee) > 0
• minmod Osher and Rudin first order gradient norm approximation
• minimal principal curvature
• maximal principal curvature
• mean curvature
• total curvature
• first eigen value of the Hessian matrix
• second eigen value of the Hessian matrix
• isophote curvature
• courant line curvature
• relative variation of the gradient along courant lines

polynomial algorithms

• evaluation of a polynomial with the Horner algorithm
• evaluation of the n first powers at a value
• slip::eval_power_nd_basis(const Vector &,const std::size_t,RandomAccessIterator,RandomAccessIterator)
• evaluation of the powers of a slip::MultivariatePolynomial<T,DIM> P until order n for a range
• evaluation of the powers of slip::MultivariatePolynomial<T,DIM> : (1,P_1,...,P_1^{order},P_2,P_2P_1,...,P_2P_k,P_2^2,..P_{dim}^{order})
• three term recurrence relation for the Legendre polynomials
• three term recurrence relation for the Legendre multivariate polynomials
• evaluation of the n first Legendre polynomials at a value
• three term recurrence relation for the Chebyshev polynomials
• three term recurrence relation for the Chebyshev multivariate polynomials
• evaluation of the n first Chebychev polynomials at a value
• evaluation of the n first second kind Chebychev polynomials at a value
• evaluation of the n first discrete Chebychev polynomials at a value
• three term recurrence relation for the Hermite polynomials
• three term recurrence relation for the Hermite multivariate polynomials
• evaluation of the n first Hermite polynomials at a value
• three term recurrence relation for the Laguerre polynomials
• three term recurrence relation for the Laguerre multivariate polynomials
• evaluation of the n first Laguerre polynomials at a value

Input/Output algorithms

Miscelleneaous algorithms

• Add a number at a file name
• Extract extension to file name
• Print a container
• Read raw data
• Write raw data

1d i/o

• Read 1d ascii data
• Write 1d ascii data

2d i/o

• Read an ascii file and convert it to a 2d container (can read matlab, octave or gnuplot ascii files)
• Write a 2d container to ascii file
• Read a grayscale image using Imagemagick
• Write a grayscale image using Imagemagick
• Read a color image using Imagemagick
• Write a color image using Imagemagick
• Write a 2d range to an ASCII tecplot file
• Read gnuplot 2d ASCII vector field
• Write a 2d vector field to an ASCII gnuplot file
• Read tecplot 2d ASCII vector field
• Write a 2d vector field to an ASCII tecplot file
• Read X and Y column of a 2d vector field ASCII tecplot file
• Read X and Y column of a 2d vector field ASCII gnuplot file

3d i/o

• Read slices of a Container3d from image files
• Writes slices of a Container3d to image files
• Read tecplot 3d ASCII vector field
• Write a 3d vector field to an ASCII tecplot file
• Read X, Y and Z column of a 3d vector field ASCII tecplot