Corrected interpolate_bilinear for lab_pixel. (#2091)

* * Corrected interpolate_bilinear for non-RGB images not to collapse into grayscale (#2089)

* * interpolate_bilinear uses now pixel_to_vector for shorter code.

* pixels now have operator!=.

* * Explicitely float interpolation

* Using C++11 static_assert() in interpolation.

* * Corrected documentation for interpolate_bilinear, interpolate_quadratic

* * Corrected formatting near interpolate_bilinear

dlib/image_processing/generic_image.h

@@ -133,6 +133,16 @@ namespace dlib
     template <typename image_type>
     struct is_rgb_image { const static bool value = pixel_traits<typename image_traits<image_type>::pixel_type>::rgb; };
 
+    template <typename image_type>
+    struct is_color_space_cartesian_image { const static bool value = 
+        pixel_traits<typename image_traits<image_type>::pixel_type>::rgb || 
+        pixel_traits<typename image_traits<image_type>::pixel_type>::lab || 
+        pixel_traits<typename image_traits<image_type>::pixel_type>::grayscale; };
+    /*
+        Tells if all color components of image pixels are in cartesian coordinates, compared to e.g. polar coordinates.
+        Polar coordinates that may require more complicated blending.
+    */
+
     template <typename image_type>
     struct is_grayscale_image { const static bool value = pixel_traits<typename image_traits<image_type>::pixel_type>::grayscale; };
 

dlib/image_transforms/interpolation.h

@@ -229,58 +229,25 @@ namespace dlib
     class interpolate_bilinear
     {
     public:
-
         template <typename T, typename image_view_type, typename pixel_type>
-        typename disable_if<is_rgb_image<image_view_type>,bool>::type operator() (
+        bool operator() (
             const image_view_type& img,
             const dlib::vector<T,2>& p,
             pixel_type& result
         ) const
         {
-            COMPILE_TIME_ASSERT(pixel_traits<typename image_view_type::pixel_type>::has_alpha == false);
-
-            const long left   = static_cast<long>(std::floor(p.x()));
-            const long top    = static_cast<long>(std::floor(p.y()));
-            const long right  = left+1;
-            const long bottom = top+1;
-
+            // Assign pixel gives special meaning to alpha channel that would break interpolation
+            static_assert(pixel_traits<typename image_view_type::pixel_type>::has_alpha == false, "Images with alpha channel not supported");
+            // Interpolation currently supports only fully cartesian (non-polar) spaces.
+            static_assert(is_color_space_cartesian_image<image_view_type>::value == true, "Non-cartesian color space used in interpolation");
 
-            // if the interpolation goes outside img 
-            if (!(left >= 0 && top >= 0 && right < img.nc() && bottom < img.nr()))
-                return false;
-
-            const double lr_frac = p.x() - left;
-            const double tb_frac = p.y() - top;
-
-            double tl = 0, tr = 0, bl = 0, br = 0;
-
-            assign_pixel(tl, img[top][left]);
-            assign_pixel(tr, img[top][right]);
-            assign_pixel(bl, img[bottom][left]);
-            assign_pixel(br, img[bottom][right]);
-            
-            double temp = (1-tb_frac)*((1-lr_frac)*tl + lr_frac*tr) + 
-                              tb_frac*((1-lr_frac)*bl + lr_frac*br);
-                            
-            assign_pixel(result, temp);
-            return true;
-        }
-
-        template <typename T, typename image_view_type, typename pixel_type>
-        typename enable_if<is_rgb_image<image_view_type>,bool>::type operator() (
-            const image_view_type& img,
-            const dlib::vector<T,2>& p,
-            pixel_type& result
-        ) const
-        {
-            COMPILE_TIME_ASSERT(pixel_traits<typename image_view_type::pixel_type>::has_alpha == false);
+            using traits = pixel_traits<typename image_view_type::pixel_type>;
 
             const long left   = static_cast<long>(std::floor(p.x()));
             const long top    = static_cast<long>(std::floor(p.y()));
             const long right  = left+1;
             const long bottom = top+1;
 
-
             // if the interpolation goes outside img 
             if (!(left >= 0 && top >= 0 && right < img.nc() && bottom < img.nr()))
                 return false;
@@ -288,36 +255,20 @@ namespace dlib
             const double lr_frac = p.x() - left;
             const double tb_frac = p.y() - top;
 
-            double tl, tr, bl, br;
-
-            tl = img[top][left].red;
-            tr = img[top][right].red;
-            bl = img[bottom][left].red;
-            br = img[bottom][right].red;
-            const double red = (1-tb_frac)*((1-lr_frac)*tl + lr_frac*tr) + 
-                                   tb_frac*((1-lr_frac)*bl + lr_frac*br);
-
-            tl = img[top][left].green;
-            tr = img[top][right].green;
-            bl = img[bottom][left].green;
-            br = img[bottom][right].green;
-            const double green = (1-tb_frac)*((1-lr_frac)*tl + lr_frac*tr) + 
-                                   tb_frac*((1-lr_frac)*bl + lr_frac*br);
-
-            tl = img[top][left].blue;
-            tr = img[top][right].blue;
-            bl = img[bottom][left].blue;
-            br = img[bottom][right].blue;
-            const double blue = (1-tb_frac)*((1-lr_frac)*tl + lr_frac*tr) + 
-                                   tb_frac*((1-lr_frac)*bl + lr_frac*br);
-                            
-            rgb_pixel temp;
-            assign_pixel(temp.red, red);
-            assign_pixel(temp.green, green);
-            assign_pixel(temp.blue, blue);
+            auto const tl = pixel_to_vector<double>(img[top][left]);
+            auto const tr = pixel_to_vector<double>(img[top][right]);
+            auto const bl = pixel_to_vector<double>(img[bottom][left]);
+            auto const br = pixel_to_vector<double>(img[bottom][right]);
+            matrix<double, traits::num, 1> pvout;
+            for (long i = 0; i < traits::num; ++i)
+                pvout(i) = (1 - tb_frac) * ((1 - lr_frac) * tl(i) + lr_frac * tr(i)) +
+                tb_frac * ((1 - lr_frac) * bl(i) + lr_frac * br(i));
+            typename image_view_type::pixel_type temp;
+            vector_to_pixel(temp, pvout);
             assign_pixel(result, temp);
             return true;
         }
+
     };
 
 // ----------------------------------------------------------------------------------------
@@ -328,46 +279,18 @@ namespace dlib
     public:
 
         template <typename T, typename image_view_type, typename pixel_type>
-        typename disable_if<is_rgb_image<image_view_type>,bool>::type operator() (
+        bool operator() (
             const image_view_type& img,
             const dlib::vector<T,2>& p,
             pixel_type& result
         ) const
         {
-            COMPILE_TIME_ASSERT(pixel_traits<typename image_view_type::pixel_type>::has_alpha == false);
-
-            const point pp(p);
+            // Assign pixel gives special meaning to alpha channel that would break interpolation
+            static_assert(pixel_traits<typename image_view_type::pixel_type>::has_alpha == false, "Images with alpha channel not supported");
+            // Interpolation currently supports only fully cartesian (non-polar) spaces.
+            static_assert(is_color_space_cartesian_image<image_view_type>::value == true, "Non-cartesian color space used in interpolation");
 
-            // if the interpolation goes outside img 
-            if (!get_rect(img).contains(grow_rect(pp,1))) 
-                return false;
-
-            const long r = pp.y();
-            const long c = pp.x();
-
-            const double temp = interpolate(p-pp, 
-                                    img[r-1][c-1],
-                                    img[r-1][c  ],
-                                    img[r-1][c+1],
-                                    img[r  ][c-1],
-                                    img[r  ][c  ],
-                                    img[r  ][c+1],
-                                    img[r+1][c-1],
-                                    img[r+1][c  ],
-                                    img[r+1][c+1]);
-
-            assign_pixel(result, temp);
-            return true;
-        }
-
-        template <typename T, typename image_view_type, typename pixel_type>
-        typename enable_if<is_rgb_image<image_view_type>,bool>::type operator() (
-            const image_view_type& img,
-            const dlib::vector<T,2>& p,
-            pixel_type& result
-        ) const
-        {
-            COMPILE_TIME_ASSERT(pixel_traits<typename image_view_type::pixel_type>::has_alpha == false);
+            using traits = pixel_traits<typename image_view_type::pixel_type>;
 
             const point pp(p);
 
@@ -378,44 +301,21 @@ namespace dlib
             const long r = pp.y();
             const long c = pp.x();
 
-            const double red = interpolate(p-pp, 
-                            img[r-1][c-1].red,
-                            img[r-1][c  ].red,
-                            img[r-1][c+1].red,
-                            img[r  ][c-1].red,
-                            img[r  ][c  ].red,
-                            img[r  ][c+1].red,
-                            img[r+1][c-1].red,
-                            img[r+1][c  ].red,
-                            img[r+1][c+1].red);
-            const double green = interpolate(p-pp, 
-                            img[r-1][c-1].green,
-                            img[r-1][c  ].green,
-                            img[r-1][c+1].green,
-                            img[r  ][c-1].green,
-                            img[r  ][c  ].green,
-                            img[r  ][c+1].green,
-                            img[r+1][c-1].green,
-                            img[r+1][c  ].green,
-                            img[r+1][c+1].green);
-            const double blue = interpolate(p-pp, 
-                            img[r-1][c-1].blue,
-                            img[r-1][c  ].blue,
-                            img[r-1][c+1].blue,
-                            img[r  ][c-1].blue,
-                            img[r  ][c  ].blue,
-                            img[r  ][c+1].blue,
-                            img[r+1][c-1].blue,
-                            img[r+1][c  ].blue,
-                            img[r+1][c+1].blue);
-
-
-            rgb_pixel temp;
-            assign_pixel(temp.red, red);
-            assign_pixel(temp.green, green);
-            assign_pixel(temp.blue, blue);
+            matrix<double, traits::num, 1> pvout;
+            for (long i = 0; i < traits::num; ++i)
+                pvout(i) = interpolate(p-pp,
+                    pixel_to_vector<double>(img[r-1][c-1])(i),
+                    pixel_to_vector<double>(img[r-1][c  ])(i),
+                    pixel_to_vector<double>(img[r-1][c+1])(i),
+                    pixel_to_vector<double>(img[r  ][c-1])(i),
+                    pixel_to_vector<double>(img[r  ][c  ])(i),
+                    pixel_to_vector<double>(img[r  ][c+1])(i),
+                    pixel_to_vector<double>(img[r+1][c-1])(i),
+                    pixel_to_vector<double>(img[r+1][c  ])(i),
+                    pixel_to_vector<double>(img[r+1][c+1])(i));
+            typename image_view_type::pixel_type temp;
+            vector_to_pixel(temp, pvout);
             assign_pixel(result, temp);
-
             return true;
         }
 

dlib/image_transforms/interpolation_abstract.h

@@ -78,14 +78,13 @@ namespace dlib
                 - image_view_type == an image_view or const_image_view object 
                 - pixel_traits<typename image_view_type::pixel_type>::has_alpha == false
                 - pixel_traits<pixel_type> is defined
+                - pixel_type uses cartesian coordinates color space
             ensures
                 - if (there is an interpolatable image location at point p in img) then
                     - #result == the interpolated pixel value from img at point p.
                     - assign_pixel() will be used to write to #result, therefore any
                       necessary color space conversion will be performed.
                     - returns true
-                    - if img contains RGB pixels then the interpolation will be in color.
-                      Otherwise, the interpolation will be performed in a grayscale mode.
                 - else
                     - returns false
         !*/
@@ -119,14 +118,13 @@ namespace dlib
                 - image_view_type == an image_view or const_image_view object. 
                 - pixel_traits<typename image_view_type::pixel_type>::has_alpha == false
                 - pixel_traits<pixel_type> is defined
+                - pixel_type uses cartesian coordinates color space
             ensures
                 - if (there is an interpolatable image location at point p in img) then
                     - #result == the interpolated pixel value from img at point p
                     - assign_pixel() will be used to write to #result, therefore any
                       necessary color space conversion will be performed.
                     - returns true
-                    - if img contains RGB pixels then the interpolation will be in color.
-                      Otherwise, the interpolation will be performed in a grayscale mode.
                 - else
                     - returns false
         !*/

dlib/pixel.h

@@ -132,6 +132,12 @@ namespace dlib
                 && this->green == that.green
                 && this->blue  == that.blue;
         }
+
+        bool operator != (const rgb_pixel& that) const
+        {
+            return !(*this == that);
+        }
+
     };
 
 // ----------------------------------------------------------------------------------------
@@ -165,6 +171,12 @@ namespace dlib
                 && this->green == that.green
                 && this->red   == that.red;
         }
+
+        bool operator != (const bgr_pixel& that) const
+        {
+            return !(*this == that);
+        }
+
     };
 
 // ----------------------------------------------------------------------------------------
@@ -199,6 +211,12 @@ namespace dlib
                 && this->blue  == that.blue
                 && this->alpha == that.alpha;
         }
+
+        bool operator != (const rgb_alpha_pixel& that) const
+        {
+            return !(*this == that);
+        }
+
     };
 
 // ----------------------------------------------------------------------------------------
@@ -229,7 +247,14 @@ namespace dlib
                 && this->s == that.s
                 && this->i == that.i;
         }
+
+        bool operator != (const hsi_pixel& that) const
+        {
+            return !(*this == that);
+        }
+
     };
+
     // ----------------------------------------------------------------------------------------
 
     struct lab_pixel
@@ -258,6 +283,12 @@ namespace dlib
                 && this->a == that.a
                 && this->b == that.b;
         }
+
+        bool operator != (const lab_pixel& that) const
+        {
+            return !(*this == that);
+        }
+
     };    
 
 // ----------------------------------------------------------------------------------------

dlib/test/image.cpp

@@ -1987,6 +1987,258 @@ namespace
         }
     }
 
+    template<typename interpolation_type = interpolate_bilinear>
+    void test_resize_image_with_interpolation()
+    {
+        {
+            matrix<unsigned char> img_s(2, 2);
+            matrix<unsigned char> img_d(3, 3);
+
+            img_s(0, 0) = 0;
+            img_s(0, 1) = 100;
+            img_s(1, 0) = 100;
+            img_s(1, 1) = 100;
+
+            resize_image(img_s, img_d, interpolation_type());
+            DLIB_TEST((img_d(0, 0) == 0));
+            DLIB_TEST((img_d(0, 1) == 50));
+            DLIB_TEST((img_d(1, 2) == 100));
+            DLIB_TEST((img_d(2, 2) == 100));
+        }
+
+        {
+            matrix<rgb_pixel> img_s(2, 2);
+            matrix<rgb_pixel> img_d(3, 3);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 10, 20, 30 };
+            img_s(1, 0) = { 10, 20, 30 };
+            img_s(1, 1) = { 10, 20, 30 };
+
+            resize_image(img_s, img_d, interpolation_type());
+            DLIB_TEST((img_d(0, 0) == rgb_pixel{ 0, 0, 0 }));
+            DLIB_TEST((img_d(0, 1) == rgb_pixel{ 5, 10, 15 }));
+            DLIB_TEST((img_d(1, 2) == rgb_pixel{ 10, 20, 30 }));
+            DLIB_TEST((img_d(2, 2) == rgb_pixel{ 10, 20, 30 }));
+        }
+
+        {
+            matrix<lab_pixel> img_s(2, 2);
+            matrix<lab_pixel> img_d(3, 3);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 100, 20, 30 };
+            img_s(1, 0) = { 100, 20, 30 };
+            img_s(1, 1) = { 100, 20, 30 };
+
+            resize_image(img_s, img_d, interpolation_type());
+            DLIB_TEST((img_d(0, 0) == lab_pixel{ 0, 0, 0 }));
+            DLIB_TEST((img_d(0, 1) == lab_pixel{ 50, 10, 15 }));
+            DLIB_TEST((img_d(1, 2) == lab_pixel{ 100, 20, 30 }));
+            DLIB_TEST((img_d(2, 2) == lab_pixel{ 100, 20, 30 }));
+        }
+
+    }
+
+    void test_null_rotate_image_with_interpolation()
+    {
+        {
+            matrix<unsigned char> img_s(3, 3);
+            matrix<unsigned char> img_d;
+
+            img_s(0, 0) = 0;
+            img_s(0, 1) = 100;
+            img_s(0, 2) = 100;
+            img_s(1, 0) = 100;
+            img_s(1, 1) = 100;
+            img_s(1, 2) = 100;
+            img_s(2, 0) = 100;
+            img_s(2, 1) = 100;
+            img_s(2, 2) = 100;
+
+            rotate_image(img_s, img_d, 0, interpolate_bilinear());
+            DLIB_TEST((img_d(0, 0) == 0));
+            DLIB_TEST((img_d(0, 1) == 100));
+            DLIB_TEST((img_d(1, 0) == 100));
+            DLIB_TEST((img_d(1, 1) == 100));
+        }
+
+        {
+            matrix<rgb_pixel> img_s(3, 3);
+            matrix<rgb_pixel> img_d(3, 3);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 10, 20, 30 };
+            img_s(0, 2) = { 10, 20, 30 };
+            img_s(1, 0) = { 10, 20, 30 };
+            img_s(1, 1) = { 10, 20, 30 };
+            img_s(1, 2) = { 10, 20, 30 };
+            img_s(2, 0) = { 10, 20, 30 };
+            img_s(2, 1) = { 10, 20, 30 };
+            img_s(2, 2) = { 10, 20, 30 };
+
+            rotate_image(img_s, img_d, 0, interpolate_bilinear());
+            DLIB_TEST((img_d(0, 0) == rgb_pixel{ 0, 0, 0 }));
+            DLIB_TEST((img_d(0, 1) == rgb_pixel{ 10, 20, 30 }));
+            DLIB_TEST((img_d(1, 0) == rgb_pixel{ 10, 20, 30 }));
+            DLIB_TEST((img_d(1, 1) == rgb_pixel{ 10, 20, 30 }));
+        }
+
+        {
+            matrix<lab_pixel> img_s(3, 3);
+            matrix<lab_pixel> img_d(3, 3);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 100, 20, 30 };
+            img_s(0, 2) = { 100, 20, 30 };
+            img_s(1, 0) = { 100, 20, 30 };
+            img_s(1, 1) = { 100, 20, 30 };
+            img_s(1, 2) = { 100, 20, 30 };
+            img_s(2, 0) = { 100, 20, 30 };
+            img_s(2, 1) = { 100, 20, 30 };
+            img_s(2, 2) = { 100, 20, 30 };
+
+            rotate_image(img_s, img_d, 0, interpolate_bilinear());
+            DLIB_TEST((img_d(0, 0) == lab_pixel{ 0, 0, 0 }));
+            DLIB_TEST((img_d(0, 1) == lab_pixel{ 100, 20, 30 }));
+            DLIB_TEST((img_d(1, 0) == lab_pixel{ 100, 20, 30 }));
+            DLIB_TEST((img_d(1, 1) == lab_pixel{ 100, 20, 30 }));
+        }
+
+    }
+
+    void test_null_rotate_image_with_interpolation_quadratic()
+    {
+        {
+            matrix<unsigned char> img_s(3, 3);
+            matrix<unsigned char> img_d;
+
+            img_s(0, 0) = 0;
+            img_s(0, 1) = 100;
+            img_s(0, 2) = 100;
+            img_s(1, 0) = 100;
+            img_s(1, 1) = 100;
+            img_s(1, 2) = 100;
+            img_s(2, 0) = 100;
+            img_s(2, 1) = 100;
+            img_s(2, 2) = 100;
+
+            rotate_image(img_s, img_d, 0, interpolate_quadratic());
+            DLIB_TEST((img_d(1, 1) == 111));
+        }
+
+        {
+            matrix<rgb_pixel> img_s(3, 3);
+            matrix<rgb_pixel> img_d(3, 3);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 10, 20, 30 };
+            img_s(0, 2) = { 10, 20, 30 };
+            img_s(1, 0) = { 10, 20, 30 };
+            img_s(1, 1) = { 10, 20, 30 };
+            img_s(1, 2) = { 10, 20, 30 };
+            img_s(2, 0) = { 10, 20, 30 };
+            img_s(2, 1) = { 10, 20, 30 };
+            img_s(2, 2) = { 10, 20, 30 };
+
+            rotate_image(img_s, img_d, 0, interpolate_quadratic());
+            DLIB_TEST((img_d(1, 1) == rgb_pixel{ 11, 22, 33 }));
+        }
+
+        {
+            matrix<lab_pixel> img_s(3, 3);
+            matrix<lab_pixel> img_d(3, 3);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 100, 20, 30 };
+            img_s(0, 2) = { 100, 20, 30 };
+            img_s(1, 0) = { 100, 20, 30 };
+            img_s(1, 1) = { 100, 20, 30 };
+            img_s(1, 2) = { 100, 20, 30 };
+            img_s(2, 0) = { 100, 20, 30 };
+            img_s(2, 1) = { 100, 20, 30 };
+            img_s(2, 2) = { 100, 20, 30 };
+
+            rotate_image(img_s, img_d, 0, interpolate_quadratic());
+            DLIB_TEST((img_d(1, 1) == lab_pixel{ 111, 22, 33 }));
+        }
+    }
+
+    void test_interpolate_bilinear()
+    {
+        {
+            matrix<unsigned char> img_s(2, 2);
+
+            img_s(0, 0) = 0;
+            img_s(0, 1) = 100;
+            img_s(1, 0) = 100;
+            img_s(1, 1) = 100;
+
+            const_image_view<matrix<unsigned char>> imgv(img_s);
+
+            unsigned char result;
+            {
+                interpolate_bilinear()(imgv, dlib::vector<double, 2>{ 0.5, 0.0 }, result);
+                DLIB_TEST(result == 50);
+            }
+            {
+                interpolate_bilinear()(imgv, dlib::vector<double, 2>{ 0.5, 0.5 }, result);
+                DLIB_TEST(result == 75);
+            }
+        }
+
+        {
+            matrix<rgb_pixel> img_s(2, 2);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 10, 20, 30 };
+            img_s(1, 0) = { 10, 20, 30 };
+            img_s(1, 1) = { 10, 20, 30 };
+
+            const_image_view<matrix<rgb_pixel>> imgv(img_s);
+
+            rgb_pixel result;
+            {
+                interpolate_bilinear()(imgv, dlib::vector<double, 2>{ 0.5, 0.0 }, result);
+                DLIB_TEST(result.red == 5);
+                DLIB_TEST(result.green == 10);
+                DLIB_TEST(result.blue == 15);
+            }
+            {
+                interpolate_bilinear()(imgv, dlib::vector<double, 2>{ 0.5, 0.5 }, result);
+                DLIB_TEST(result.red == 7);
+                DLIB_TEST(result.green == 15);
+                DLIB_TEST(result.blue == 22);
+            }
+        }
+
+        {
+            matrix<lab_pixel> img_s(2, 2);
+
+            img_s(0, 0) = { 0, 0, 0 };
+            img_s(0, 1) = { 100, 20, 30 };
+            img_s(1, 0) = { 100, 20, 30 };
+            img_s(1, 1) = { 100, 20, 30 };
+
+            const_image_view<matrix<lab_pixel>> imgv(img_s);
+
+            lab_pixel result;
+            {
+                interpolate_bilinear()(imgv, dlib::vector<double, 2>{ 0.5, 0.0 }, result);
+                DLIB_TEST(result.l == 50);
+                DLIB_TEST(result.a == 10);
+                DLIB_TEST(result.b == 15);
+            }
+            {
+                interpolate_bilinear()(imgv, dlib::vector<double, 2>{ 0.5, 0.5 }, result);
+                DLIB_TEST(result.l == 75);
+                DLIB_TEST(result.a == 15);
+                DLIB_TEST(result.b == 22);
+            }
+        }
+    }
+    
+
 // ----------------------------------------------------------------------------------------
 
     class image_tester : public tester
@@ -2086,6 +2338,10 @@ namespace
             }
 
             test_partition_pixels();
+            test_resize_image_with_interpolation<interpolate_bilinear>();
+            test_null_rotate_image_with_interpolation();
+            test_null_rotate_image_with_interpolation_quadratic();
+            test_interpolate_bilinear();
         }
     } a;
 

dlib/test/serialize.cpp

@@ -15,28 +15,6 @@
 
 #include "tester.h"
 
-namespace dlib
-{
-    static bool operator!=(const rgb_pixel& a, const rgb_pixel& b)
-    {
-        return !(a.red==b.red && a.green==b.green && a.blue==b.blue);
-    }
-    static bool operator!=(const bgr_pixel& a, const bgr_pixel& b)
-    {
-        return !(a.red==b.red && a.green==b.green && a.blue==b.blue);
-    }
-
-    static bool operator!=(const hsi_pixel& a, const hsi_pixel& b)
-    {
-        return !(a.h==b.h && a.s==b.s && a.i==b.i);
-    }
-    static bool operator!=(const rgb_alpha_pixel& a, const rgb_alpha_pixel& b)
-    {
-        return !(a.red==b.red && a.green==b.green && a.blue==b.blue && a.alpha==b.alpha);
-    }
-
-}
-
 namespace  
 {