kernel.cc

/*  kernel.cc

    Mark Jenkinson, FMRIB Image Analysis Group

    Copyright (C) 2001 University of Oxford  */

/*  CCOPYRIGHT  */

#include "kernel.h"
#include "miscmaths.h"

namespace MISCMATHS {

  set<kernelstorage*, kernelstorage::comparer> kernel::existingkernels;  

  //////// Support function /////////

  float kernelval(float x, int w, const ColumnVector& kernel)
  {
    // linearly interpolates to get the kernel at the point (x)
    //   given the half-width w
    if (fabs(x)>w) return 0.0;
    float halfnk = (kernel.Nrows()-1.0)/2.0;
    float dn = x/w*halfnk + halfnk + 1.0;
    int n = (int) floor(dn);
    dn -= n;
    if (n>(kernel.Nrows()-1)) return 0.0;
    if (n<1) return 0.0;
    
    return kernel(n)*(1.0-dn) + kernel(n+1)*dn;
  }
  
  inline bool in_bounds(const ColumnVector& data, int index)
  { return ( (index>=1) && (index<=data.Nrows())); }
  
  inline bool in_bounds(const ColumnVector& data, float index)
  { return ( ((int)floor(index)>=1) && ((int)ceil(index)<=data.Nrows())); }
  
  float sincfn(float x)
  {
    if (fabs(x)<1e-7) { return 1.0-fabs(x); }
    float y=M_PI*x;
    return sin(y)/y;
  }
  
  float hanning(float x, int w)
  {  // w is half-width
    if (fabs(x)>w) 
      return 0.0;
    else
      return (0.5 + 0.5 *cos(M_PI*x/w));
  }
  
  float blackman(float x, int w)
  {  // w is half-width
    if (fabs(x)>w) 
      return 0.0;
    else
      return (0.42 + 0.5 *cos(M_PI*x/w) + 0.08*cos(2.0*M_PI*x/w));
  }
  
  float rectangular(float x, int w)
  {  // w is half-width
    if (fabs(x)>w) 
      return 0.0;
    else
      return 1.0;
  }

  ColumnVector sinckernel1D(const string& sincwindowtype, int w, int n)
  {  // w is full-width
    int nstore = n;
    if (nstore<1) nstore=1;
    ColumnVector ker(nstore);
    int hw = (w-1)/2; // convert to half-width
    // set x between +/- width
    float halfnk = (nstore-1.0)/2.0;
    for (int n=1; n<=nstore; n++) {
      float x=(n-halfnk-1)/halfnk*hw;
      if ( (sincwindowtype=="hanning") || (sincwindowtype=="h") ) {
	ker(n) = sincfn(x)*hanning(x,hw);
      } else if ( (sincwindowtype=="blackman") || (sincwindowtype=="b") ) {
	ker(n) = sincfn(x)*blackman(x,hw);
      } else if ( (sincwindowtype=="rectangular") || (sincwindowtype=="r") ) {
	ker(n) = sincfn(x)*rectangular(x,hw);
      } else {
	cerr << "ERROR: Unrecognised sinc window type - using Blackman" << endl;
	ker = sinckernel1D("b",w,nstore);
	return ker;
      }
    }
    return ker;
  }

  
  kernel sinckernel(const string& sincwindowtype, int w, int nstore) 
  {
    kernel sinck;
    sinck = sinckernel(sincwindowtype,w,w,w,nstore);
    return sinck;
  }


  kernel sinckernel(const string& sincwindowtype,
		    int wx, int wy, int wz, int nstore)
  { // widths are full-widths
    kernel sinckern;
    if (nstore<1) nstore=1;

    // convert all widths to half-widths
    int hwx = (wx-1)/2;
    int hwy = (wy-1)/2;
    int hwz = (wz-1)/2;

    ColumnVector kx, ky, kz;
    // calculate kernels
    kx = sinckernel1D(sincwindowtype,wx,nstore);
    ky = sinckernel1D(sincwindowtype,wy,nstore);
    kz = sinckernel1D(sincwindowtype,wz,nstore);
    
    sinckern.setkernel(kx,ky,kz,hwx,hwy,hwz);
    return sinckern;
  }

  // dummy fn for now
  float extrapolate_1d(const ColumnVector& data, const int index)
  {
    float extrapval;

    if (in_bounds(data, index))
      extrapval = data(index);
    else if (in_bounds(data, index-1))
      extrapval = data(data.Nrows());
    else if (in_bounds(data, index+1))
      extrapval = data(1);
    else
      extrapval = mean(data).AsScalar();

    return extrapval;
  }
  
  // basic trilinear call
  float interpolate_1d(const ColumnVector& data, const float index)
  {
    float interpval;
    int low_bound = (int)floor(index);
    int high_bound = (int)ceil(index); 

    if (in_bounds(data, index))
      interpval = data(low_bound) + (index - low_bound)*(data(high_bound) - data(low_bound));
    else
      interpval = extrapolate_1d(data, round(index));

    return interpval;
  }

    
  //////// Spline Support /////////

  float hermiteinterpolation_1d(const ColumnVector& data, int p1, int p4, float t)
  {
    // Q(t) = (2t^3 - 3t^2 + 1)P_1 + (-2t^3 + 3t^2)P_4 + (t^3 - 2t^2 + t)R_1 + (t^3 - t^2)R_4
    // inputs: points P_1, P_4; tangents R_1, R_4; interpolation index t;

    float retval, r1 = 0.0, r4 = 0.0;
    
    if (!in_bounds(data,p1) || !in_bounds(data,p4)) {
      cerr << "Hermite Interpolation - ERROR: One or more indicies lie outside the data range. Returning ZERO" << endl;
      retval = 0.0;
    } else if ((t < 0) || (t > 1)) {
      cerr << "Hermite Interpolation - ERROR: Interpolation index must lie between 0 and 1. Returning ZERO" << endl;
      retval = 0.0;
      /*    } else if (t == 0.0) {
	    retval = data(p1);
	    } else if (t == 1.0) {
	    retval = data(p4);
      */   
    } else {
      r1 = 0.5 * (extrapolate_1d(data, p1) - extrapolate_1d(data, p1 - 1)) + 0.5 * (extrapolate_1d(data, p1 + 1) - extrapolate_1d(data, p1));// tangent @ P_1
      r4 = 0.5 * (extrapolate_1d(data, p4) - extrapolate_1d(data, p4 - 1)) + 0.5 * (extrapolate_1d(data, p4 + 1) - extrapolate_1d(data, p4));// tangent @ P_4
      
      float t2 = t*t; float t3 = t2*t;
      retval = (2*t3 - 3*t2 + 1)*data(p1) + (-2*t3 + 3*t2)*data(p4) + (t3 - 2*t2 + t)*r1 + (t3 - t2)*r4;
    }

    // cerr << "p1, p4, t, r1, r4 = " << p1 << ", " << p4 << ", " << t << ", " << r1 << ", " << r4 << endl;
    
    return retval;
  }


  //////// Kernel Interpolation Call /////////

  float kernelinterpolation_1d(const ColumnVector& data, float index, const ColumnVector& userkernel, int width)
  {
    int widthx = (width - 1)/2;
    // kernel half-width  (i.e. range is +/- w)
    int ix0;
    ix0 = (int) floor(index);
    
    int wx(widthx);
    vector<float> storex(2*wx+1);
    for (int d=-wx; d<=wx; d++) 
       storex[d+wx] = kernelval((index-ix0+d),wx,userkernel);

    float convsum=0.0, interpval=0.0, kersum=0.0;
    
    int xj;
    for (int x1=ix0-wx; x1<=ix0+wx; x1++) {
      if (in_bounds(data, x1)) {
	xj=ix0-x1+wx;
	float kerfac = storex[xj];
	convsum += data(x1) * kerfac;
	kersum += kerfac;
      }
    }

    if ( (fabs(kersum)>1e-9) ) {
      interpval = convsum / kersum;
    } else {
      interpval = (float) extrapolate_1d(data, ix0);
    }
    return interpval;
  }
  
  ////// Kernel wrappers //////

  float kernelinterpolation_1d(const ColumnVector& data, float index)
  {
    ColumnVector userkernel = sinckernel1D("hanning", 7, 1201);
    return kernelinterpolation_1d(data, index, userkernel, 7);
  }

  float kernelinterpolation_1d(RowVector data, float index)
  {
    ColumnVector userkernel = sinckernel1D("hanning", 7, 1201);
    return kernelinterpolation_1d(data.t(), index, userkernel, 7);
  }
}