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IM: Math Utilities

From IM - An Imaging Tool

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Math Utilities
[Utilities]

Detailed Description

See im_color.h


Functions

template<class T, class TU>
T imZeroOrderDecimation (int width, int height, T *map, float xl, float yl, float box_width, float box_height, TU Dummy)
template<class T, class TU>
T imBilinearDecimation (int width, int height, T *map, float xl, float yl, float box_width, float box_height, TU Dummy)
template<class T>
T imZeroOrderInterpolation (int width, int height, T *map, float xl, float yl)
template<class T>
T imBilinearInterpolation (int width, int height, T *map, float xl, float yl)
template<class T, class TU>
T imBicubicInterpolation (int width, int height, T *map, float xl, float yl, TU Dummy)
template<class T>
void imMinMax (const T *map, int count, T &min, T &max)

Function Documentation

template<class T, class TU>
T imZeroOrderDecimation (  int  width,
int  height,
T *  map,
float  xl,
float  yl,
float  box_width,
float  box_height,
TU  Dummy
)  [inline]
 

Does Zero Order Decimation (Mean). 

00045 {
00046   int x0,x1,y0,y1;
00047   (void)Dummy;
00048 
00049   x0 = (int)floor(xl - box_width/2.0 - 0.5) + 1;
00050   y0 = (int)floor(yl - box_height/2.0 - 0.5) + 1;
00051   x1 = (int)floor(xl + box_width/2.0 - 0.5);
00052   y1 = (int)floor(yl + box_height/2.0 - 0.5);
00053 
00054   if (x0 == x1) x1++;
00055   if (y0 == y1) y1++;
00056 
00057   x0 = x0<0? 0: x0>width-1? width-1: x0;
00058   y0 = y0<0? 0: y0>height-1? height-1: y0;
00059   x1 = x1<0? 0: x1>width-1? width-1: x1;
00060   y1 = y1<0? 0: y1>height-1? height-1: y1;
00061 
00062   TU Value;
00063   int Count = 0;
00064 
00065   Value = 0;
00066 
00067   for (int y = y0; y <= y1; y++)
00068   {
00069     for (int x = x0; x <= x1; x++)
00070     {
00071       Value += map[y*width+x];
00072       Count++;
00073     }
00074   }
00075 
00076   if (Count == 0)
00077   {
00078     Value = 0;
00079     return (T)Value;
00080   }
00081 
00082   return (T)(Value/(float)Count);
00083 }

template<class T, class TU>
T imBilinearDecimation (  int  width,
int  height,
T *  map,
float  xl,
float  yl,
float  box_width,
float  box_height,
TU  Dummy
)  [inline]
 

Does Bilinear Decimation. 

00089 {
00090   int x0,x1,y0,y1;
00091   (void)Dummy;
00092 
00093   x0 = (int)floor(xl - box_width/2.0 - 0.5) + 1;
00094   y0 = (int)floor(yl - box_height/2.0 - 0.5) + 1;
00095   x1 = (int)floor(xl + box_width/2.0 - 0.5);
00096   y1 = (int)floor(yl + box_height/2.0 - 0.5);
00097 
00098   if (x0 == x1) x1++;
00099   if (y0 == y1) y1++;
00100 
00101   x0 = x0<0? 0: x0>width-1? width-1: x0;
00102   y0 = y0<0? 0: y0>height-1? height-1: y0;
00103   x1 = x1<0? 0: x1>width-1? width-1: x1;
00104   y1 = y1<0? 0: y1>height-1? height-1: y1;
00105 
00106   TU Value, LineValue;
00107   float LineNorm, Norm, dxr, dyr;
00108 
00109   Value = 0;
00110   Norm = 0;
00111 
00112   for (int y = y0; y <= y1; y++)
00113   {
00114     dyr = yl - (y+0.5f);
00115     if (dyr < 0) dyr *= -1;
00116 
00117     LineValue = 0;
00118     LineNorm = 0;
00119 
00120     for (int x = x0; x <= x1; x++)
00121     {
00122       dxr = xl - (x+0.5f);
00123       if (dxr < 0) dxr *= -1;
00124 
00125       LineValue += map[y*width+x] * dxr;
00126       LineNorm += dxr;
00127     }
00128 
00129     Value += LineValue * dyr;
00130     Norm += dyr * LineNorm;
00131   }
00132 
00133   if (Norm == 0)
00134   {
00135     Value = 0;
00136     return (T)Value;
00137   }
00138 
00139   return (T)(Value/Norm);
00140 }

template<class T>
T imZeroOrderInterpolation (  int  width,
int  height,
T *  map,
float  xl,
float  yl
)  [inline]
 

Does Zero Order Interpolation (Nearest Neighborhood). 

00146 {
00147   int x0 = (int)(xl-0.5f);
00148   int y0 = (int)(yl-0.5f);
00149   x0 = x0<0? 0: x0>width-1? width-1: x0;
00150   y0 = y0<0? 0: y0>height-1? height-1: y0;
00151   return map[y0*width + x0];
00152 }

template<class T>
T imBilinearInterpolation (  int  width,
int  height,
T *  map,
float  xl,
float  yl
)  [inline]
 

Does Bilinear Interpolation. 

00158 {
00159   int x0, y0, x1, y1;
00160   float t, u;
00161 
00162   if (xl < 0.5)
00163   {
00164     x1 = x0 = 0; 
00165     t = 0;
00166   }
00167   else if (xl > width-0.5)
00168   {
00169     x1 = x0 = width-1;
00170     t = 0;
00171   }
00172   else
00173   {
00174     x0 = (int)(xl-0.5f);
00175     x1 = x0+1;
00176     t = xl - (x0+0.5f);
00177   }
00178 
00179   if (yl < 0.5)
00180   {
00181     y1 = y0 = 0; 
00182     u = 0;
00183   }
00184   else if (yl > height-0.5)
00185   {
00186     y1 = y0 = height-1;
00187     u = 0;
00188   }
00189   else
00190   {
00191     y0 = (int)(yl-0.5f);
00192     y1 = y0+1;
00193     u = yl - (y0+0.5f);
00194   }
00195 
00196   T fll = map[y0*width + x0];
00197   T fhl = map[y0*width + x1];
00198   T flh = map[y1*width + x0];
00199   T fhh = map[y1*width + x1];
00200 
00201   return (T)((fhh - flh - fhl + fll) * u * t +
00202                          (fhl - fll) * t +
00203                          (flh - fll) * u +
00204                                 fll);
00205 }

template<class T, class TU>
T imBicubicInterpolation (  int  width,
int  height,
T *  map,
float  xl,
float  yl,
TU  Dummy
)  [inline]
 

Does Bicubic Interpolation. 

00211 {
00212   int x0, y0, x1, y1, x2, y2;
00213   float t, u;
00214   (void)Dummy;
00215 
00216   if (xl < 0.5)
00217   {
00218     x2 = x1 = x0 = 0; 
00219     t = 0;
00220   }
00221   else if (xl > width-0.5)
00222   {
00223     x2 = x1 = x0 = width-1;
00224     t = 0;
00225   }
00226   else
00227   {
00228     x0 = (int)(xl-0.5f);
00229     x1 = x0-1; 
00230     if (x1 < 0) x1 = 0;
00231     x2 = x0+2; // 4 pixels (-1 0 +1 +2) 
00232     if (x2 > width-1) x2 = width-1;
00233     t = xl - (x0+0.5f);
00234   }
00235 
00236   if (yl < 0.5)
00237   {
00238     y2 = y1 = y0 = 0; 
00239     u = 0;
00240   }
00241   else if (yl > height-0.5)
00242   {
00243     y2 = y1 = y0 = height-1;
00244     u = 0;
00245   }
00246   else
00247   {
00248     y0 = (int)(yl-0.5f);
00249     y1 = y0-1;
00250     if (y1 < 0) y1 = 0;
00251     y2 = y0+2; // 4 pixels (-1 0 +1 +2)
00252     if (y2 > height-1) y2 = height-1;
00253     u = yl - (y0+0.5f);
00254   }
00255 
00256   float CX[4], CY[4];
00257 
00258   // Optimize calculations
00259   {
00260     float x, x2, x3;
00261 
00262 #define C0 (-x3 + 2.0f*x2 - x)
00263 #define C1 ( x3 - 2.0f*x2 + 1.0f)
00264 #define C2 (-x3 + x2 + x)
00265 #define C3 ( x3 - x2)
00266 
00267     x = t;
00268     x2 = x*x; x3 = x2*x;
00269     CX[0] = C0; CX[1] = C1; CX[2] = C2; CX[3] = C3;
00270 
00271     x = u;
00272     x2 = x*x; x3 = x2*x;
00273     CY[0] = C0; CY[1] = C1; CY[2] = C2; CY[3] = C3;
00274 
00275 #undef C0
00276 #undef C1
00277 #undef C2
00278 #undef C3
00279   }
00280 
00281   TU LineValue, Value;
00282   float LineNorm, Norm;
00283 
00284   Value = 0;
00285   Norm = 0;
00286 
00287   for (int y = y1; y <= y2; y++)
00288   {
00289     LineValue = 0;
00290     LineNorm = 0;
00291 
00292     for (int x = x1; x <= x2; x++)
00293     {
00294       LineValue += map[y*width+x] * CX[x-x1];
00295       LineNorm += CX[x-x1];
00296     }
00297 
00298     Value += LineValue * CY[y-y1];
00299     Norm += CY[y-y1] * LineNorm;
00300   }
00301 
00302   if (Norm == 0)
00303   {
00304     Value = 0;
00305     return (T)Value;
00306   }
00307 
00308   Value = (Value/Norm);
00309 
00310   int size = sizeof(T); 
00311   if (size == 1)
00312     return (T)(Value<=(TU)0? (TU)0: Value<=(TU)255? Value: (TU)255);
00313   else
00314     return (T)(Value);
00315 }

template<class T>
void imMinMax (  const T *  map,
int  count,
T &  min,
T &  max
)  [inline]
 

Calculates minimum and maximum values. 

00321 {
00322   min = *map++;
00323   max = min;
00324   for (int i = 1; i < count; i++)
00325   {
00326     T value = *map++;
00327 
00328     if (value > max)
00329       max = value;
00330     else if (value < min)
00331       min = value;
00332   }
00333 }


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