math

Class BSpline

java.lang.Object

math.BSpline

public class BSpline
extends Object

This class implements basic operations to work with cubic B-splines.

Author:

Ignacio Arganda-Carreras - ignacio.arganda@gmail.com

Constructor Summary

Constructors

Constructor and Description
BSpline()

Method Summary

Modifier and Type	Method and Description
static double[]	convertToInterpCoef(double[] input, double[] poles, double tolerance) Convert to interpolation coefficients
static double[]	convertToSamples(double[] coef, double[] samples) Convert the spline coefficients to samples
static int	factorial(int n) Factorial
static double[]	finDiffAS(double[] c) Finite Difference.
static double	initialAntiCausalCoefficient(double[] c, double z) Get initial anti-causal coefficients
static double	initialCausalCoefficient(double[] c, double z, double tolerance) Initialization of causal coefficients for mirror boundary conditions
static double[]	integAS(double[] c) Begin computation of the running sums.
static double	integSA(double[] c, double[] z) Begin computation of the running sums.
static double	mean(double[] A) Calculate mean value on the period (2*length(A)-2)
static double[]	resampling(double[] input, int nInput, int nOut, double scale, int n1, int nt) Geometric transform and resampling
static double[]	resize1D(double[] input, int n, int n1, int n2, double scale, boolean coefOrSamples) Ref: A.
static double[]	tableOfPoles(int splineDegree) Recover the poles from a lookup table
static double[]	tableOfSamples(int splineDegree) Recover the B-spline samples values from a lookup table

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

BSpline

public BSpline()

Method Detail

resize1D

public static double[] resize1D(double[] input,
                                int n,
                                int n1,
                                int n2,
                                double scale,
                                boolean coefOrSamples)

Ref: A. Muñoz-Barrutia, T. Blu, M. Unser, "Least-Squares Image Resizing Using Finite Differences," IEEE Transactions on Image Processing, vol. 10, n. 9, September 2001.

Use: out(x) = input(x/scale); scale > 1 expansion; a < 1 reduction.

Use n=n2:

• if (n1==-1) the standard method (interpolation and resampling) is applied.
• If (n=n1=n2), the orthogonal projection is computed. The error is the minimum in the least-squares sense.
• If ((n1 > -1) && (n1<n2)), the oblique projection is computed. The error is slightly greater than the case above.

Parameters:

input - input signal

n - degree of the interpolation spline. It can vary from 0 to 3.

n1 - degree of the analysis spline. It can vary from -1 to 3.

n2 - degree of the synthesis spline. It can vary from 0 to 3.

scale - zoom factor (scale > 1 expansion; scale < 1 reduction)

coefOrSamples - if working with coefficients coefOrSamples is true; if working with samples coefOrSamples is false

Returns:

out signal

convertToSamples

public static double[] convertToSamples(double[] coef,
                                        double[] samples)

Convert the spline coefficients to samples

Parameters:

coef - input coefficients values

samples - output samples

Returns:

finDiffAS

public static double[] finDiffAS(double[] c)

Finite Difference. Anti-symmetric input boundary conditions. Symmetric output boundary conditions.

Parameters:

c - input signal

Returns:

output signal

resampling

public static double[] resampling(double[] input,
                                  int nInput,
                                  int nOut,
                                  double scale,
                                  int n1,
                                  int nt)

Geometric transform and resampling

Parameters:

input - input signal

nInput - length of the input signal

nOut - length of the resize signal

scale - expansion/reduction

n1 - degree of the analysis spline

nt - (n+n1+1)

Returns:

re-sampled signal

factorial

public static int factorial(int n)

Factorial

Parameters:

n -

Returns:

n factorial

integAS

public static double[] integAS(double[] c)

Begin computation of the running sums. The input boundary conditions are anti-symmetric. The output boundary conditions are symmetric.

Parameters:

c - input coefficients

Returns:

sums

integSA

public static double integSA(double[] c,
                             double[] z)

Begin computation of the running sums. The input boundary conditions are symmetric. The output boundary conditions are anti-symmetric.

Parameters:

c - coefficients

z - sums

Returns:

mean value on the period (2*length(c)-2)

mean

public static double mean(double[] A)

Calculate mean value on the period (2*length(A)-2)

Parameters:

A -

Returns:

mean value on the period (2*length(A)-2)

convertToInterpCoef

public static double[] convertToInterpCoef(double[] input,
                                           double[] poles,
                                           double tolerance)

Convert to interpolation coefficients

Parameters:

input -

poles -

tolerance -

Returns:

initialAntiCausalCoefficient

public static double initialAntiCausalCoefficient(double[] c,
                                                  double z)

Get initial anti-causal coefficients

Parameters:

c - coefficients

z - pole

Returns:

value of the initial anti-causal coefficient

initialCausalCoefficient

public static double initialCausalCoefficient(double[] c,
                                              double z,
                                              double tolerance)

Initialization of causal coefficients for mirror boundary conditions

Parameters:

c - coefficients

z - pole

tolerance - accuracy

Returns:

value of the initial causal coefficient for the given accuracy

tableOfPoles

public static double[] tableOfPoles(int splineDegree)

Recover the poles from a lookup table

Parameters:

splineDegree - degree of the spline

Returns:

Pole values

tableOfSamples

public static double[] tableOfSamples(int splineDegree)

Recover the B-spline samples values from a lookup table

Parameters:

splineDegree - degree of the spline

Returns:

Value of the samples