xref: /external/opencv3/modules/core/include/opencv2/core/types.hpp

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#ifndef __OPENCV_CORE_TYPES_HPP__
#define __OPENCV_CORE_TYPES_HPP__

#ifndef __cplusplus
#  error types.hpp header must be compiled as C++
#endif

#include <climits>
#include <cfloat>
#include <vector>

#include "opencv2/core/cvdef.h"
#include "opencv2/core/cvstd.hpp"
#include "opencv2/core/matx.hpp"

namespace cv
{

//! @addtogroup core_basic
//! @{

//////////////////////////////// Complex //////////////////////////////

/** @brief  A complex number class.

  The template class is similar and compatible with std::complex, however it provides slightly
  more convenient access to the real and imaginary parts using through the simple field access, as opposite
  to std::complex::real() and std::complex::imag().
*/
template<typename _Tp> class Complex
{
public:

    //! constructors
    Complex();
    Complex( _Tp _re, _Tp _im = 0 );

    //! conversion to another data type
    template<typename T2> operator Complex<T2>() const;
    //! conjugation
    Complex conj() const;

    _Tp re, im; //< the real and the imaginary parts
};

typedef Complex<float> Complexf;
typedef Complex<double> Complexd;

template<typename _Tp> class DataType< Complex<_Tp> >
{
public:
    typedef Complex<_Tp> value_type;
    typedef value_type   work_type;
    typedef _Tp          channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 2,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels) };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// Point_ ////////////////////////////////

/** @brief Template class for 2D points specified by its coordinates `x` and `y`.

An instance of the class is interchangeable with C structures, CvPoint and CvPoint2D32f . There is
also a cast operator to convert point coordinates to the specified type. The conversion from
floating-point coordinates to integer coordinates is done by rounding. Commonly, the conversion
uses this operation for each of the coordinates. Besides the class members listed in the
declaration above, the following operations on points are implemented:
@code
    pt1 = pt2 + pt3;
    pt1 = pt2 - pt3;
    pt1 = pt2 * a;
    pt1 = a * pt2;
    pt1 = pt2 / a;
    pt1 += pt2;
    pt1 -= pt2;
    pt1 *= a;
    pt1 /= a;
    double value = norm(pt); // L2 norm
    pt1 == pt2;
    pt1 != pt2;
@endcode
For your convenience, the following type aliases are defined:
@code
    typedef Point_<int> Point2i;
    typedef Point2i Point;
    typedef Point_<float> Point2f;
    typedef Point_<double> Point2d;
@endcode
Example:
@code
    Point2f a(0.3f, 0.f), b(0.f, 0.4f);
    Point pt = (a + b)*10.f;
    cout << pt.x << ", " << pt.y << endl;
@endcode
*/
template<typename _Tp> class Point_
{
public:
    typedef _Tp value_type;

    // various constructors
    Point_();
    Point_(_Tp _x, _Tp _y);
    Point_(const Point_& pt);
    Point_(const Size_<_Tp>& sz);
    Point_(const Vec<_Tp, 2>& v);

    Point_& operator = (const Point_& pt);
    //! conversion to another data type
    template<typename _Tp2> operator Point_<_Tp2>() const;

    //! conversion to the old-style C structures
    operator Vec<_Tp, 2>() const;

    //! dot product
    _Tp dot(const Point_& pt) const;
    //! dot product computed in double-precision arithmetics
    double ddot(const Point_& pt) const;
    //! cross-product
    double cross(const Point_& pt) const;
    //! checks whether the point is inside the specified rectangle
    bool inside(const Rect_<_Tp>& r) const;

    _Tp x, y; //< the point coordinates
};

typedef Point_<int> Point2i;
typedef Point_<float> Point2f;
typedef Point_<double> Point2d;
typedef Point2i Point;

template<typename _Tp> class DataType< Point_<_Tp> >
{
public:
    typedef Point_<_Tp>                               value_type;
    typedef Point_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                       channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 2,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// Point3_ ////////////////////////////////

/** @brief Template class for 3D points specified by its coordinates `x`, `y` and `z`.

An instance of the class is interchangeable with the C structure CvPoint2D32f . Similarly to
Point_ , the coordinates of 3D points can be converted to another type. The vector arithmetic and
comparison operations are also supported.

The following Point3_\<\> aliases are available:
@code
    typedef Point3_<int> Point3i;
    typedef Point3_<float> Point3f;
    typedef Point3_<double> Point3d;
@endcode
@see cv::Point3i, cv::Point3f and cv::Point3d
*/
template<typename _Tp> class Point3_
{
public:
    typedef _Tp value_type;

    // various constructors
    Point3_();
    Point3_(_Tp _x, _Tp _y, _Tp _z);
    Point3_(const Point3_& pt);
    explicit Point3_(const Point_<_Tp>& pt);
    Point3_(const Vec<_Tp, 3>& v);

    Point3_& operator = (const Point3_& pt);
    //! conversion to another data type
    template<typename _Tp2> operator Point3_<_Tp2>() const;
    //! conversion to cv::Vec<>
    operator Vec<_Tp, 3>() const;

    //! dot product
    _Tp dot(const Point3_& pt) const;
    //! dot product computed in double-precision arithmetics
    double ddot(const Point3_& pt) const;
    //! cross product of the 2 3D points
    Point3_ cross(const Point3_& pt) const;

    _Tp x, y, z; //< the point coordinates
};

typedef Point3_<int> Point3i;
typedef Point3_<float> Point3f;
typedef Point3_<double> Point3d;

template<typename _Tp> class DataType< Point3_<_Tp> >
{
public:
    typedef Point3_<_Tp>                               value_type;
    typedef Point3_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                        channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 3,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// Size_ ////////////////////////////////

/** @brief Template class for specifying the size of an image or rectangle.

The class includes two members called width and height. The structure can be converted to and from
the old OpenCV structures CvSize and CvSize2D32f . The same set of arithmetic and comparison
operations as for Point_ is available.

OpenCV defines the following Size_\<\> aliases:
@code
    typedef Size_<int> Size2i;
    typedef Size2i Size;
    typedef Size_<float> Size2f;
@endcode
*/
template<typename _Tp> class Size_
{
public:
    typedef _Tp value_type;

    //! various constructors
    Size_();
    Size_(_Tp _width, _Tp _height);
    Size_(const Size_& sz);
    Size_(const Point_<_Tp>& pt);

    Size_& operator = (const Size_& sz);
    //! the area (width*height)
    _Tp area() const;

    //! conversion of another data type.
    template<typename _Tp2> operator Size_<_Tp2>() const;

    _Tp width, height; // the width and the height
};

typedef Size_<int> Size2i;
typedef Size_<float> Size2f;
typedef Size_<double> Size2d;
typedef Size2i Size;

template<typename _Tp> class DataType< Size_<_Tp> >
{
public:
    typedef Size_<_Tp>                               value_type;
    typedef Size_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                      channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 2,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// Rect_ ////////////////////////////////

/** @brief Template class for 2D rectangles

described by the following parameters:
-   Coordinates of the top-left corner. This is a default interpretation of Rect_::x and Rect_::y
    in OpenCV. Though, in your algorithms you may count x and y from the bottom-left corner.
-   Rectangle width and height.

OpenCV typically assumes that the top and left boundary of the rectangle are inclusive, while the
right and bottom boundaries are not. For example, the method Rect_::contains returns true if

\f[x  \leq pt.x < x+width,
      y  \leq pt.y < y+height\f]

Virtually every loop over an image ROI in OpenCV (where ROI is specified by Rect_\<int\> ) is
implemented as:
@code
    for(int y = roi.y; y < roi.y + roi.height; y++)
        for(int x = roi.x; x < roi.x + roi.width; x++)
        {
            // ...
        }
@endcode
In addition to the class members, the following operations on rectangles are implemented:
-   \f$\texttt{rect} = \texttt{rect} \pm \texttt{point}\f$ (shifting a rectangle by a certain offset)
-   \f$\texttt{rect} = \texttt{rect} \pm \texttt{size}\f$ (expanding or shrinking a rectangle by a
    certain amount)
-   rect += point, rect -= point, rect += size, rect -= size (augmenting operations)
-   rect = rect1 & rect2 (rectangle intersection)
-   rect = rect1 | rect2 (minimum area rectangle containing rect1 and rect2 )
-   rect &= rect1, rect |= rect1 (and the corresponding augmenting operations)
-   rect == rect1, rect != rect1 (rectangle comparison)

This is an example how the partial ordering on rectangles can be established (rect1 \f$\subseteq\f$
rect2):
@code
    template<typename _Tp> inline bool
    operator <= (const Rect_<_Tp>& r1, const Rect_<_Tp>& r2)
    {
        return (r1 & r2) == r1;
    }
@endcode
For your convenience, the Rect_\<\> alias is available: cv::Rect
*/
template<typename _Tp> class Rect_
{
public:
    typedef _Tp value_type;

    //! various constructors
    Rect_();
    Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height);
    Rect_(const Rect_& r);
    Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz);
    Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2);

    Rect_& operator = ( const Rect_& r );
    //! the top-left corner
    Point_<_Tp> tl() const;
    //! the bottom-right corner
    Point_<_Tp> br() const;

    //! size (width, height) of the rectangle
    Size_<_Tp> size() const;
    //! area (width*height) of the rectangle
    _Tp area() const;

    //! conversion to another data type
    template<typename _Tp2> operator Rect_<_Tp2>() const;

    //! checks whether the rectangle contains the point
    bool contains(const Point_<_Tp>& pt) const;

    _Tp x, y, width, height; //< the top-left corner, as well as width and height of the rectangle
};

typedef Rect_<int> Rect2i;
typedef Rect_<float> Rect2f;
typedef Rect_<double> Rect2d;
typedef Rect2i Rect;

template<typename _Tp> class DataType< Rect_<_Tp> >
{
public:
    typedef Rect_<_Tp>                               value_type;
    typedef Rect_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                      channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 4,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



///////////////////////////// RotatedRect /////////////////////////////

/** @brief The class represents rotated (i.e. not up-right) rectangles on a plane.

Each rectangle is specified by the center point (mass center), length of each side (represented by
cv::Size2f structure) and the rotation angle in degrees.

The sample below demonstrates how to use RotatedRect:
@code
    Mat image(200, 200, CV_8UC3, Scalar(0));
    RotatedRect rRect = RotatedRect(Point2f(100,100), Size2f(100,50), 30);

    Point2f vertices[4];
    rRect.points(vertices);
    for (int i = 0; i < 4; i++)
        line(image, vertices[i], vertices[(i+1)%4], Scalar(0,255,0));

    Rect brect = rRect.boundingRect();
    rectangle(image, brect, Scalar(255,0,0));

    imshow("rectangles", image);
    waitKey(0);
@endcode
![image](pics/rotatedrect.png)

@sa CamShift, fitEllipse, minAreaRect, CvBox2D
*/
class CV_EXPORTS RotatedRect
{
public:
    //! various constructors
    RotatedRect();
    /**
    @param center The rectangle mass center.
    @param size Width and height of the rectangle.
    @param angle The rotation angle in a clockwise direction. When the angle is 0, 90, 180, 270 etc.,
    the rectangle becomes an up-right rectangle.
    */
    RotatedRect(const Point2f& center, const Size2f& size, float angle);
    /**
    Any 3 end points of the RotatedRect. They must be given in order (either clockwise or
    anticlockwise).
     */
    RotatedRect(const Point2f& point1, const Point2f& point2, const Point2f& point3);

    /** returns 4 vertices of the rectangle
    @param pts The points array for storing rectangle vertices.
    */
    void points(Point2f pts[]) const;
    //! returns the minimal up-right rectangle containing the rotated rectangle
    Rect boundingRect() const;

    Point2f center; //< the rectangle mass center
    Size2f size;    //< width and height of the rectangle
    float angle;    //< the rotation angle. When the angle is 0, 90, 180, 270 etc., the rectangle becomes an up-right rectangle.
};

template<> class DataType< RotatedRect >
{
public:
    typedef RotatedRect  value_type;
    typedef value_type   work_type;
    typedef float        channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = (int)sizeof(value_type)/sizeof(channel_type), // 5
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// Range /////////////////////////////////

/** @brief Template class specifying a continuous subsequence (slice) of a sequence.

The class is used to specify a row or a column span in a matrix ( Mat ) and for many other purposes.
Range(a,b) is basically the same as a:b in Matlab or a..b in Python. As in Python, start is an
inclusive left boundary of the range and end is an exclusive right boundary of the range. Such a
half-opened interval is usually denoted as \f$[start,end)\f$ .

The static method Range::all() returns a special variable that means "the whole sequence" or "the
whole range", just like " : " in Matlab or " ... " in Python. All the methods and functions in
OpenCV that take Range support this special Range::all() value. But, of course, in case of your own
custom processing, you will probably have to check and handle it explicitly:
@code
    void my_function(..., const Range& r, ....)
    {
        if(r == Range::all()) {
            // process all the data
        }
        else {
            // process [r.start, r.end)
        }
    }
@endcode
*/
class CV_EXPORTS Range
{
public:
    Range();
    Range(int _start, int _end);
    int size() const;
    bool empty() const;
    static Range all();

    int start, end;
};

template<> class DataType<Range>
{
public:
    typedef Range      value_type;
    typedef value_type work_type;
    typedef int        channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 2,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// Scalar_ ///////////////////////////////

/** @brief Template class for a 4-element vector derived from Vec.

Being derived from Vec\<_Tp, 4\> , Scalar_ and Scalar can be used just as typical 4-element
vectors. In addition, they can be converted to/from CvScalar . The type Scalar is widely used in
OpenCV to pass pixel values.
*/
template<typename _Tp> class Scalar_ : public Vec<_Tp, 4>
{
public:
    //! various constructors
    Scalar_();
    Scalar_(_Tp v0, _Tp v1, _Tp v2=0, _Tp v3=0);
    Scalar_(_Tp v0);

    template<typename _Tp2, int cn>
    Scalar_(const Vec<_Tp2, cn>& v);

    //! returns a scalar with all elements set to v0
    static Scalar_<_Tp> all(_Tp v0);

    //! conversion to another data type
    template<typename T2> operator Scalar_<T2>() const;

    //! per-element product
    Scalar_<_Tp> mul(const Scalar_<_Tp>& a, double scale=1 ) const;

    // returns (v0, -v1, -v2, -v3)
    Scalar_<_Tp> conj() const;

    // returns true iff v1 == v2 == v3 == 0
    bool isReal() const;
};

typedef Scalar_<double> Scalar;

template<typename _Tp> class DataType< Scalar_<_Tp> >
{
public:
    typedef Scalar_<_Tp>                               value_type;
    typedef Scalar_<typename DataType<_Tp>::work_type> work_type;
    typedef _Tp                                        channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = 4,
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



/////////////////////////////// KeyPoint ////////////////////////////////

/** @brief Data structure for salient point detectors.

The class instance stores a keypoint, i.e. a point feature found by one of many available keypoint
detectors, such as Harris corner detector, cv::FAST, cv::StarDetector, cv::SURF, cv::SIFT,
cv::LDetector etc.

The keypoint is characterized by the 2D position, scale (proportional to the diameter of the
neighborhood that needs to be taken into account), orientation and some other parameters. The
keypoint neighborhood is then analyzed by another algorithm that builds a descriptor (usually
represented as a feature vector). The keypoints representing the same object in different images
can then be matched using cv::KDTree or another method.
*/
class CV_EXPORTS_W_SIMPLE KeyPoint
{
public:
    //! the default constructor
    CV_WRAP KeyPoint();
    /**
    @param _pt x & y coordinates of the keypoint
    @param _size keypoint diameter
    @param _angle keypoint orientation
    @param _response keypoint detector response on the keypoint (that is, strength of the keypoint)
    @param _octave pyramid octave in which the keypoint has been detected
    @param _class_id object id
     */
    KeyPoint(Point2f _pt, float _size, float _angle=-1, float _response=0, int _octave=0, int _class_id=-1);
    /**
    @param x x-coordinate of the keypoint
    @param y y-coordinate of the keypoint
    @param _size keypoint diameter
    @param _angle keypoint orientation
    @param _response keypoint detector response on the keypoint (that is, strength of the keypoint)
    @param _octave pyramid octave in which the keypoint has been detected
    @param _class_id object id
     */
    CV_WRAP KeyPoint(float x, float y, float _size, float _angle=-1, float _response=0, int _octave=0, int _class_id=-1);

    size_t hash() const;

    /**
    This method converts vector of keypoints to vector of points or the reverse, where each keypoint is
    assigned the same size and the same orientation.

    @param keypoints Keypoints obtained from any feature detection algorithm like SIFT/SURF/ORB
    @param points2f Array of (x,y) coordinates of each keypoint
    @param keypointIndexes Array of indexes of keypoints to be converted to points. (Acts like a mask to
    convert only specified keypoints)
    */
    CV_WRAP static void convert(const std::vector<KeyPoint>& keypoints,
                                CV_OUT std::vector<Point2f>& points2f,
                                const std::vector<int>& keypointIndexes=std::vector<int>());
    /** @overload
    @param points2f Array of (x,y) coordinates of each keypoint
    @param keypoints Keypoints obtained from any feature detection algorithm like SIFT/SURF/ORB
    @param size keypoint diameter
    @param response keypoint detector response on the keypoint (that is, strength of the keypoint)
    @param octave pyramid octave in which the keypoint has been detected
    @param class_id object id
    */
    CV_WRAP static void convert(const std::vector<Point2f>& points2f,
                                CV_OUT std::vector<KeyPoint>& keypoints,
                                float size=1, float response=1, int octave=0, int class_id=-1);

    /**
    This method computes overlap for pair of keypoints. Overlap is the ratio between area of keypoint
    regions' intersection and area of keypoint regions' union (considering keypoint region as circle).
    If they don't overlap, we get zero. If they coincide at same location with same size, we get 1.
    @param kp1 First keypoint
    @param kp2 Second keypoint
    */
    CV_WRAP static float overlap(const KeyPoint& kp1, const KeyPoint& kp2);

    CV_PROP_RW Point2f pt; //!< coordinates of the keypoints
    CV_PROP_RW float size; //!< diameter of the meaningful keypoint neighborhood
    CV_PROP_RW float angle; //!< computed orientation of the keypoint (-1 if not applicable);
                            //!< it's in [0,360) degrees and measured relative to
                            //!< image coordinate system, ie in clockwise.
    CV_PROP_RW float response; //!< the response by which the most strong keypoints have been selected. Can be used for the further sorting or subsampling
    CV_PROP_RW int octave; //!< octave (pyramid layer) from which the keypoint has been extracted
    CV_PROP_RW int class_id; //!< object class (if the keypoints need to be clustered by an object they belong to)
};

template<> class DataType<KeyPoint>
{
public:
    typedef KeyPoint      value_type;
    typedef float         work_type;
    typedef float         channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = (int)(sizeof(value_type)/sizeof(channel_type)), // 7
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



//////////////////////////////// DMatch /////////////////////////////////

/** @brief Class for matching keypoint descriptors

query descriptor index, train descriptor index, train image index, and distance between
descriptors.
*/
class CV_EXPORTS_W_SIMPLE DMatch
{
public:
    CV_WRAP DMatch();
    CV_WRAP DMatch(int _queryIdx, int _trainIdx, float _distance);
    CV_WRAP DMatch(int _queryIdx, int _trainIdx, int _imgIdx, float _distance);

    CV_PROP_RW int queryIdx; // query descriptor index
    CV_PROP_RW int trainIdx; // train descriptor index
    CV_PROP_RW int imgIdx;   // train image index

    CV_PROP_RW float distance;

    // less is better
    bool operator<(const DMatch &m) const;
};

template<> class DataType<DMatch>
{
public:
    typedef DMatch      value_type;
    typedef int         work_type;
    typedef int         channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = (int)(sizeof(value_type)/sizeof(channel_type)), // 4
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};



///////////////////////////// TermCriteria //////////////////////////////

/** @brief The class defining termination criteria for iterative algorithms.

You can initialize it by default constructor and then override any parameters, or the structure may
be fully initialized using the advanced variant of the constructor.
*/
class CV_EXPORTS TermCriteria
{
public:
    /**
      Criteria type, can be one of: COUNT, EPS or COUNT + EPS
    */
    enum Type
    {
        COUNT=1, //!< the maximum number of iterations or elements to compute
        MAX_ITER=COUNT, //!< ditto
        EPS=2 //!< the desired accuracy or change in parameters at which the iterative algorithm stops
    };

    //! default constructor
    TermCriteria();
    /**
    @param type The type of termination criteria, one of TermCriteria::Type
    @param maxCount The maximum number of iterations or elements to compute.
    @param epsilon The desired accuracy or change in parameters at which the iterative algorithm stops.
    */
    TermCriteria(int type, int maxCount, double epsilon);

    int type; //!< the type of termination criteria: COUNT, EPS or COUNT + EPS
    int maxCount; // the maximum number of iterations/elements
    double epsilon; // the desired accuracy
};


//! @} core_basic

///////////////////////// raster image moments //////////////////////////

//! @addtogroup imgproc_shape
//! @{

/** @brief struct returned by cv::moments

The spatial moments \f$\texttt{Moments::m}_{ji}\f$ are computed as:

\f[\texttt{m} _{ji}= \sum _{x,y}  \left ( \texttt{array} (x,y)  \cdot x^j  \cdot y^i \right )\f]

The central moments \f$\texttt{Moments::mu}_{ji}\f$ are computed as:

\f[\texttt{mu} _{ji}= \sum _{x,y}  \left ( \texttt{array} (x,y)  \cdot (x -  \bar{x} )^j  \cdot (y -  \bar{y} )^i \right )\f]

where \f$(\bar{x}, \bar{y})\f$ is the mass center:

\f[\bar{x} = \frac{\texttt{m}_{10}}{\texttt{m}_{00}} , \; \bar{y} = \frac{\texttt{m}_{01}}{\texttt{m}_{00}}\f]

The normalized central moments \f$\texttt{Moments::nu}_{ij}\f$ are computed as:

\f[\texttt{nu} _{ji}= \frac{\texttt{mu}_{ji}}{\texttt{m}_{00}^{(i+j)/2+1}} .\f]

@note
\f$\texttt{mu}_{00}=\texttt{m}_{00}\f$, \f$\texttt{nu}_{00}=1\f$
\f$\texttt{nu}_{10}=\texttt{mu}_{10}=\texttt{mu}_{01}=\texttt{mu}_{10}=0\f$ , hence the values are not
stored.

The moments of a contour are defined in the same way but computed using the Green's formula (see
<http://en.wikipedia.org/wiki/Green_theorem>). So, due to a limited raster resolution, the moments
computed for a contour are slightly different from the moments computed for the same rasterized
contour.

@note
Since the contour moments are computed using Green formula, you may get seemingly odd results for
contours with self-intersections, e.g. a zero area (m00) for butterfly-shaped contours.
 */
class CV_EXPORTS_W_MAP Moments
{
public:
    //! the default constructor
    Moments();
    //! the full constructor
    Moments(double m00, double m10, double m01, double m20, double m11,
            double m02, double m30, double m21, double m12, double m03 );
    ////! the conversion from CvMoments
    //Moments( const CvMoments& moments );
    ////! the conversion to CvMoments
    //operator CvMoments() const;

    //! @name spatial moments
    //! @{
    CV_PROP_RW double  m00, m10, m01, m20, m11, m02, m30, m21, m12, m03;
    //! @}

    //! @name central moments
    //! @{
    CV_PROP_RW double  mu20, mu11, mu02, mu30, mu21, mu12, mu03;
    //! @}

    //! @name central normalized moments
    //! @{
    CV_PROP_RW double  nu20, nu11, nu02, nu30, nu21, nu12, nu03;
    //! @}
};

template<> class DataType<Moments>
{
public:
    typedef Moments     value_type;
    typedef double      work_type;
    typedef double      channel_type;

    enum { generic_type = 0,
           depth        = DataType<channel_type>::depth,
           channels     = (int)(sizeof(value_type)/sizeof(channel_type)), // 24
           fmt          = DataType<channel_type>::fmt + ((channels - 1) << 8),
           type         = CV_MAKETYPE(depth, channels)
         };

    typedef Vec<channel_type, channels> vec_type;
};

//! @} imgproc_shape

//! @cond IGNORED

/////////////////////////////////////////////////////////////////////////
///////////////////////////// Implementation ////////////////////////////
/////////////////////////////////////////////////////////////////////////

//////////////////////////////// Complex ////////////////////////////////

template<typename _Tp> inline
Complex<_Tp>::Complex()
    : re(0), im(0) {}

template<typename _Tp> inline
Complex<_Tp>::Complex( _Tp _re, _Tp _im )
    : re(_re), im(_im) {}

template<typename _Tp> template<typename T2> inline
Complex<_Tp>::operator Complex<T2>() const
{
    return Complex<T2>(saturate_cast<T2>(re), saturate_cast<T2>(im));
}

template<typename _Tp> inline
Complex<_Tp> Complex<_Tp>::conj() const
{
    return Complex<_Tp>(re, -im);
}


template<typename _Tp> static inline
bool operator == (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return a.re == b.re && a.im == b.im;
}

template<typename _Tp> static inline
bool operator != (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return a.re != b.re || a.im != b.im;
}

template<typename _Tp> static inline
Complex<_Tp> operator + (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return Complex<_Tp>( a.re + b.re, a.im + b.im );
}

template<typename _Tp> static inline
Complex<_Tp>& operator += (Complex<_Tp>& a, const Complex<_Tp>& b)
{
    a.re += b.re; a.im += b.im;
    return a;
}

template<typename _Tp> static inline
Complex<_Tp> operator - (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return Complex<_Tp>( a.re - b.re, a.im - b.im );
}

template<typename _Tp> static inline
Complex<_Tp>& operator -= (Complex<_Tp>& a, const Complex<_Tp>& b)
{
    a.re -= b.re; a.im -= b.im;
    return a;
}

template<typename _Tp> static inline
Complex<_Tp> operator - (const Complex<_Tp>& a)
{
    return Complex<_Tp>(-a.re, -a.im);
}

template<typename _Tp> static inline
Complex<_Tp> operator * (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return Complex<_Tp>( a.re*b.re - a.im*b.im, a.re*b.im + a.im*b.re );
}

template<typename _Tp> static inline
Complex<_Tp> operator * (const Complex<_Tp>& a, _Tp b)
{
    return Complex<_Tp>( a.re*b, a.im*b );
}

template<typename _Tp> static inline
Complex<_Tp> operator * (_Tp b, const Complex<_Tp>& a)
{
    return Complex<_Tp>( a.re*b, a.im*b );
}

template<typename _Tp> static inline
Complex<_Tp> operator + (const Complex<_Tp>& a, _Tp b)
{
    return Complex<_Tp>( a.re + b, a.im );
}

template<typename _Tp> static inline
Complex<_Tp> operator - (const Complex<_Tp>& a, _Tp b)
{ return Complex<_Tp>( a.re - b, a.im ); }

template<typename _Tp> static inline
Complex<_Tp> operator + (_Tp b, const Complex<_Tp>& a)
{
    return Complex<_Tp>( a.re + b, a.im );
}

template<typename _Tp> static inline
Complex<_Tp> operator - (_Tp b, const Complex<_Tp>& a)
{
    return Complex<_Tp>( b - a.re, -a.im );
}

template<typename _Tp> static inline
Complex<_Tp>& operator += (Complex<_Tp>& a, _Tp b)
{
    a.re += b; return a;
}

template<typename _Tp> static inline
Complex<_Tp>& operator -= (Complex<_Tp>& a, _Tp b)
{
    a.re -= b; return a;
}

template<typename _Tp> static inline
Complex<_Tp>& operator *= (Complex<_Tp>& a, _Tp b)
{
    a.re *= b; a.im *= b; return a;
}

template<typename _Tp> static inline
double abs(const Complex<_Tp>& a)
{
    return std::sqrt( (double)a.re*a.re + (double)a.im*a.im);
}

template<typename _Tp> static inline
Complex<_Tp> operator / (const Complex<_Tp>& a, const Complex<_Tp>& b)
{
    double t = 1./((double)b.re*b.re + (double)b.im*b.im);
    return Complex<_Tp>( (_Tp)((a.re*b.re + a.im*b.im)*t),
                        (_Tp)((-a.re*b.im + a.im*b.re)*t) );
}

template<typename _Tp> static inline
Complex<_Tp>& operator /= (Complex<_Tp>& a, const Complex<_Tp>& b)
{
    return (a = a / b);
}

template<typename _Tp> static inline
Complex<_Tp> operator / (const Complex<_Tp>& a, _Tp b)
{
    _Tp t = (_Tp)1/b;
    return Complex<_Tp>( a.re*t, a.im*t );
}

template<typename _Tp> static inline
Complex<_Tp> operator / (_Tp b, const Complex<_Tp>& a)
{
    return Complex<_Tp>(b)/a;
}

template<typename _Tp> static inline
Complex<_Tp> operator /= (const Complex<_Tp>& a, _Tp b)
{
    _Tp t = (_Tp)1/b;
    a.re *= t; a.im *= t; return a;
}



//////////////////////////////// 2D Point ///////////////////////////////

template<typename _Tp> inline
Point_<_Tp>::Point_()
    : x(0), y(0) {}

template<typename _Tp> inline
Point_<_Tp>::Point_(_Tp _x, _Tp _y)
    : x(_x), y(_y) {}

template<typename _Tp> inline
Point_<_Tp>::Point_(const Point_& pt)
    : x(pt.x), y(pt.y) {}

template<typename _Tp> inline
Point_<_Tp>::Point_(const Size_<_Tp>& sz)
    : x(sz.width), y(sz.height) {}

template<typename _Tp> inline
Point_<_Tp>::Point_(const Vec<_Tp,2>& v)
    : x(v[0]), y(v[1]) {}

template<typename _Tp> inline
Point_<_Tp>& Point_<_Tp>::operator = (const Point_& pt)
{
    x = pt.x; y = pt.y;
    return *this;
}

template<typename _Tp> template<typename _Tp2> inline
Point_<_Tp>::operator Point_<_Tp2>() const
{
    return Point_<_Tp2>(saturate_cast<_Tp2>(x), saturate_cast<_Tp2>(y));
}

template<typename _Tp> inline
Point_<_Tp>::operator Vec<_Tp, 2>() const
{
    return Vec<_Tp, 2>(x, y);
}

template<typename _Tp> inline
_Tp Point_<_Tp>::dot(const Point_& pt) const
{
    return saturate_cast<_Tp>(x*pt.x + y*pt.y);
}

template<typename _Tp> inline
double Point_<_Tp>::ddot(const Point_& pt) const
{
    return (double)x*pt.x + (double)y*pt.y;
}

template<typename _Tp> inline
double Point_<_Tp>::cross(const Point_& pt) const
{
    return (double)x*pt.y - (double)y*pt.x;
}

template<typename _Tp> inline bool
Point_<_Tp>::inside( const Rect_<_Tp>& r ) const
{
    return r.contains(*this);
}


template<typename _Tp> static inline
Point_<_Tp>& operator += (Point_<_Tp>& a, const Point_<_Tp>& b)
{
    a.x += b.x;
    a.y += b.y;
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator -= (Point_<_Tp>& a, const Point_<_Tp>& b)
{
    a.x -= b.x;
    a.y -= b.y;
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator *= (Point_<_Tp>& a, int b)
{
    a.x = saturate_cast<_Tp>(a.x * b);
    a.y = saturate_cast<_Tp>(a.y * b);
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator *= (Point_<_Tp>& a, float b)
{
    a.x = saturate_cast<_Tp>(a.x * b);
    a.y = saturate_cast<_Tp>(a.y * b);
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator *= (Point_<_Tp>& a, double b)
{
    a.x = saturate_cast<_Tp>(a.x * b);
    a.y = saturate_cast<_Tp>(a.y * b);
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator /= (Point_<_Tp>& a, int b)
{
    a.x = saturate_cast<_Tp>(a.x / b);
    a.y = saturate_cast<_Tp>(a.y / b);
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator /= (Point_<_Tp>& a, float b)
{
    a.x = saturate_cast<_Tp>(a.x / b);
    a.y = saturate_cast<_Tp>(a.y / b);
    return a;
}

template<typename _Tp> static inline
Point_<_Tp>& operator /= (Point_<_Tp>& a, double b)
{
    a.x = saturate_cast<_Tp>(a.x / b);
    a.y = saturate_cast<_Tp>(a.y / b);
    return a;
}

template<typename _Tp> static inline
double norm(const Point_<_Tp>& pt)
{
    return std::sqrt((double)pt.x*pt.x + (double)pt.y*pt.y);
}

template<typename _Tp> static inline
bool operator == (const Point_<_Tp>& a, const Point_<_Tp>& b)
{
    return a.x == b.x && a.y == b.y;
}

template<typename _Tp> static inline
bool operator != (const Point_<_Tp>& a, const Point_<_Tp>& b)
{
    return a.x != b.x || a.y != b.y;
}

template<typename _Tp> static inline
Point_<_Tp> operator + (const Point_<_Tp>& a, const Point_<_Tp>& b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(a.x + b.x), saturate_cast<_Tp>(a.y + b.y) );
}

template<typename _Tp> static inline
Point_<_Tp> operator - (const Point_<_Tp>& a, const Point_<_Tp>& b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(a.x - b.x), saturate_cast<_Tp>(a.y - b.y) );
}

template<typename _Tp> static inline
Point_<_Tp> operator - (const Point_<_Tp>& a)
{
    return Point_<_Tp>( saturate_cast<_Tp>(-a.x), saturate_cast<_Tp>(-a.y) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (const Point_<_Tp>& a, int b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (int a, const Point_<_Tp>& b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(b.x*a), saturate_cast<_Tp>(b.y*a) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (const Point_<_Tp>& a, float b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (float a, const Point_<_Tp>& b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(b.x*a), saturate_cast<_Tp>(b.y*a) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (const Point_<_Tp>& a, double b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (double a, const Point_<_Tp>& b)
{
    return Point_<_Tp>( saturate_cast<_Tp>(b.x*a), saturate_cast<_Tp>(b.y*a) );
}

template<typename _Tp> static inline
Point_<_Tp> operator * (const Matx<_Tp, 2, 2>& a, const Point_<_Tp>& b)
{
    Matx<_Tp, 2, 1> tmp = a * Vec<_Tp,2>(b.x, b.y);
    return Point_<_Tp>(tmp.val[0], tmp.val[1]);
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (const Matx<_Tp, 3, 3>& a, const Point_<_Tp>& b)
{
    Matx<_Tp, 3, 1> tmp = a * Vec<_Tp,3>(b.x, b.y, 1);
    return Point3_<_Tp>(tmp.val[0], tmp.val[1], tmp.val[2]);
}

template<typename _Tp> static inline
Point_<_Tp> operator / (const Point_<_Tp>& a, int b)
{
    Point_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}

template<typename _Tp> static inline
Point_<_Tp> operator / (const Point_<_Tp>& a, float b)
{
    Point_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}

template<typename _Tp> static inline
Point_<_Tp> operator / (const Point_<_Tp>& a, double b)
{
    Point_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}



//////////////////////////////// 3D Point ///////////////////////////////

template<typename _Tp> inline
Point3_<_Tp>::Point3_()
    : x(0), y(0), z(0) {}

template<typename _Tp> inline
Point3_<_Tp>::Point3_(_Tp _x, _Tp _y, _Tp _z)
    : x(_x), y(_y), z(_z) {}

template<typename _Tp> inline
Point3_<_Tp>::Point3_(const Point3_& pt)
    : x(pt.x), y(pt.y), z(pt.z) {}

template<typename _Tp> inline
Point3_<_Tp>::Point3_(const Point_<_Tp>& pt)
    : x(pt.x), y(pt.y), z(_Tp()) {}

template<typename _Tp> inline
Point3_<_Tp>::Point3_(const Vec<_Tp, 3>& v)
    : x(v[0]), y(v[1]), z(v[2]) {}

template<typename _Tp> template<typename _Tp2> inline
Point3_<_Tp>::operator Point3_<_Tp2>() const
{
    return Point3_<_Tp2>(saturate_cast<_Tp2>(x), saturate_cast<_Tp2>(y), saturate_cast<_Tp2>(z));
}

template<typename _Tp> inline
Point3_<_Tp>::operator Vec<_Tp, 3>() const
{
    return Vec<_Tp, 3>(x, y, z);
}

template<typename _Tp> inline
Point3_<_Tp>& Point3_<_Tp>::operator = (const Point3_& pt)
{
    x = pt.x; y = pt.y; z = pt.z;
    return *this;
}

template<typename _Tp> inline
_Tp Point3_<_Tp>::dot(const Point3_& pt) const
{
    return saturate_cast<_Tp>(x*pt.x + y*pt.y + z*pt.z);
}

template<typename _Tp> inline
double Point3_<_Tp>::ddot(const Point3_& pt) const
{
    return (double)x*pt.x + (double)y*pt.y + (double)z*pt.z;
}

template<typename _Tp> inline
Point3_<_Tp> Point3_<_Tp>::cross(const Point3_<_Tp>& pt) const
{
    return Point3_<_Tp>(y*pt.z - z*pt.y, z*pt.x - x*pt.z, x*pt.y - y*pt.x);
}


template<typename _Tp> static inline
Point3_<_Tp>& operator += (Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    a.x += b.x;
    a.y += b.y;
    a.z += b.z;
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator -= (Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    a.x -= b.x;
    a.y -= b.y;
    a.z -= b.z;
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator *= (Point3_<_Tp>& a, int b)
{
    a.x = saturate_cast<_Tp>(a.x * b);
    a.y = saturate_cast<_Tp>(a.y * b);
    a.z = saturate_cast<_Tp>(a.z * b);
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator *= (Point3_<_Tp>& a, float b)
{
    a.x = saturate_cast<_Tp>(a.x * b);
    a.y = saturate_cast<_Tp>(a.y * b);
    a.z = saturate_cast<_Tp>(a.z * b);
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator *= (Point3_<_Tp>& a, double b)
{
    a.x = saturate_cast<_Tp>(a.x * b);
    a.y = saturate_cast<_Tp>(a.y * b);
    a.z = saturate_cast<_Tp>(a.z * b);
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator /= (Point3_<_Tp>& a, int b)
{
    a.x = saturate_cast<_Tp>(a.x / b);
    a.y = saturate_cast<_Tp>(a.y / b);
    a.z = saturate_cast<_Tp>(a.z / b);
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator /= (Point3_<_Tp>& a, float b)
{
    a.x = saturate_cast<_Tp>(a.x / b);
    a.y = saturate_cast<_Tp>(a.y / b);
    a.z = saturate_cast<_Tp>(a.z / b);
    return a;
}

template<typename _Tp> static inline
Point3_<_Tp>& operator /= (Point3_<_Tp>& a, double b)
{
    a.x = saturate_cast<_Tp>(a.x / b);
    a.y = saturate_cast<_Tp>(a.y / b);
    a.z = saturate_cast<_Tp>(a.z / b);
    return a;
}

template<typename _Tp> static inline
double norm(const Point3_<_Tp>& pt)
{
    return std::sqrt((double)pt.x*pt.x + (double)pt.y*pt.y + (double)pt.z*pt.z);
}

template<typename _Tp> static inline
bool operator == (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    return a.x == b.x && a.y == b.y && a.z == b.z;
}

template<typename _Tp> static inline
bool operator != (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    return a.x != b.x || a.y != b.y || a.z != b.z;
}

template<typename _Tp> static inline
Point3_<_Tp> operator + (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(a.x + b.x), saturate_cast<_Tp>(a.y + b.y), saturate_cast<_Tp>(a.z + b.z));
}

template<typename _Tp> static inline
Point3_<_Tp> operator - (const Point3_<_Tp>& a, const Point3_<_Tp>& b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(a.x - b.x), saturate_cast<_Tp>(a.y - b.y), saturate_cast<_Tp>(a.z - b.z));
}

template<typename _Tp> static inline
Point3_<_Tp> operator - (const Point3_<_Tp>& a)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(-a.x), saturate_cast<_Tp>(-a.y), saturate_cast<_Tp>(-a.z) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (const Point3_<_Tp>& a, int b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(a.x*b), saturate_cast<_Tp>(a.y*b), saturate_cast<_Tp>(a.z*b) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (int a, const Point3_<_Tp>& b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(b.x * a), saturate_cast<_Tp>(b.y * a), saturate_cast<_Tp>(b.z * a) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (const Point3_<_Tp>& a, float b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(a.x * b), saturate_cast<_Tp>(a.y * b), saturate_cast<_Tp>(a.z * b) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (float a, const Point3_<_Tp>& b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(b.x * a), saturate_cast<_Tp>(b.y * a), saturate_cast<_Tp>(b.z * a) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (const Point3_<_Tp>& a, double b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(a.x * b), saturate_cast<_Tp>(a.y * b), saturate_cast<_Tp>(a.z * b) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (double a, const Point3_<_Tp>& b)
{
    return Point3_<_Tp>( saturate_cast<_Tp>(b.x * a), saturate_cast<_Tp>(b.y * a), saturate_cast<_Tp>(b.z * a) );
}

template<typename _Tp> static inline
Point3_<_Tp> operator * (const Matx<_Tp, 3, 3>& a, const Point3_<_Tp>& b)
{
    Matx<_Tp, 3, 1> tmp = a * Vec<_Tp,3>(b.x, b.y, b.z);
    return Point3_<_Tp>(tmp.val[0], tmp.val[1], tmp.val[2]);
}

template<typename _Tp> static inline
Matx<_Tp, 4, 1> operator * (const Matx<_Tp, 4, 4>& a, const Point3_<_Tp>& b)
{
    return a * Matx<_Tp, 4, 1>(b.x, b.y, b.z, 1);
}

template<typename _Tp> static inline
Point3_<_Tp> operator / (const Point3_<_Tp>& a, int b)
{
    Point3_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}

template<typename _Tp> static inline
Point3_<_Tp> operator / (const Point3_<_Tp>& a, float b)
{
    Point3_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}

template<typename _Tp> static inline
Point3_<_Tp> operator / (const Point3_<_Tp>& a, double b)
{
    Point3_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}



////////////////////////////////// Size /////////////////////////////////

template<typename _Tp> inline
Size_<_Tp>::Size_()
    : width(0), height(0) {}

template<typename _Tp> inline
Size_<_Tp>::Size_(_Tp _width, _Tp _height)
    : width(_width), height(_height) {}

template<typename _Tp> inline
Size_<_Tp>::Size_(const Size_& sz)
    : width(sz.width), height(sz.height) {}

template<typename _Tp> inline
Size_<_Tp>::Size_(const Point_<_Tp>& pt)
    : width(pt.x), height(pt.y) {}

template<typename _Tp> template<typename _Tp2> inline
Size_<_Tp>::operator Size_<_Tp2>() const
{
    return Size_<_Tp2>(saturate_cast<_Tp2>(width), saturate_cast<_Tp2>(height));
}

template<typename _Tp> inline
Size_<_Tp>& Size_<_Tp>::operator = (const Size_<_Tp>& sz)
{
    width = sz.width; height = sz.height;
    return *this;
}

template<typename _Tp> inline
_Tp Size_<_Tp>::area() const
{
    return width * height;
}

template<typename _Tp> static inline
Size_<_Tp>& operator *= (Size_<_Tp>& a, _Tp b)
{
    a.width *= b;
    a.height *= b;
    return a;
}

template<typename _Tp> static inline
Size_<_Tp> operator * (const Size_<_Tp>& a, _Tp b)
{
    Size_<_Tp> tmp(a);
    tmp *= b;
    return tmp;
}

template<typename _Tp> static inline
Size_<_Tp>& operator /= (Size_<_Tp>& a, _Tp b)
{
    a.width /= b;
    a.height /= b;
    return a;
}

template<typename _Tp> static inline
Size_<_Tp> operator / (const Size_<_Tp>& a, _Tp b)
{
    Size_<_Tp> tmp(a);
    tmp /= b;
    return tmp;
}

template<typename _Tp> static inline
Size_<_Tp>& operator += (Size_<_Tp>& a, const Size_<_Tp>& b)
{
    a.width += b.width;
    a.height += b.height;
    return a;
}

template<typename _Tp> static inline
Size_<_Tp> operator + (const Size_<_Tp>& a, const Size_<_Tp>& b)
{
    Size_<_Tp> tmp(a);
    tmp += b;
    return tmp;
}

template<typename _Tp> static inline
Size_<_Tp>& operator -= (Size_<_Tp>& a, const Size_<_Tp>& b)
{
    a.width -= b.width;
    a.height -= b.height;
    return a;
}

template<typename _Tp> static inline
Size_<_Tp> operator - (const Size_<_Tp>& a, const Size_<_Tp>& b)
{
    Size_<_Tp> tmp(a);
    tmp -= b;
    return tmp;
}

template<typename _Tp> static inline
bool operator == (const Size_<_Tp>& a, const Size_<_Tp>& b)
{
    return a.width == b.width && a.height == b.height;
}

template<typename _Tp> static inline
bool operator != (const Size_<_Tp>& a, const Size_<_Tp>& b)
{
    return !(a == b);
}



////////////////////////////////// Rect /////////////////////////////////

template<typename _Tp> inline
Rect_<_Tp>::Rect_()
    : x(0), y(0), width(0), height(0) {}

template<typename _Tp> inline
Rect_<_Tp>::Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height)
    : x(_x), y(_y), width(_width), height(_height) {}

template<typename _Tp> inline
Rect_<_Tp>::Rect_(const Rect_<_Tp>& r)
    : x(r.x), y(r.y), width(r.width), height(r.height) {}

template<typename _Tp> inline
Rect_<_Tp>::Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz)
    : x(org.x), y(org.y), width(sz.width), height(sz.height) {}

template<typename _Tp> inline
Rect_<_Tp>::Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2)
{
    x = std::min(pt1.x, pt2.x);
    y = std::min(pt1.y, pt2.y);
    width = std::max(pt1.x, pt2.x) - x;
    height = std::max(pt1.y, pt2.y) - y;
}

template<typename _Tp> inline
Rect_<_Tp>& Rect_<_Tp>::operator = ( const Rect_<_Tp>& r )
{
    x = r.x;
    y = r.y;
    width = r.width;
    height = r.height;
    return *this;
}

template<typename _Tp> inline
Point_<_Tp> Rect_<_Tp>::tl() const
{
    return Point_<_Tp>(x,y);
}

template<typename _Tp> inline
Point_<_Tp> Rect_<_Tp>::br() const
{
    return Point_<_Tp>(x + width, y + height);
}

template<typename _Tp> inline
Size_<_Tp> Rect_<_Tp>::size() const
{
    return Size_<_Tp>(width, height);
}

template<typename _Tp> inline
_Tp Rect_<_Tp>::area() const
{
    return width * height;
}

template<typename _Tp> template<typename _Tp2> inline
Rect_<_Tp>::operator Rect_<_Tp2>() const
{
    return Rect_<_Tp2>(saturate_cast<_Tp2>(x), saturate_cast<_Tp2>(y), saturate_cast<_Tp2>(width), saturate_cast<_Tp2>(height));
}

template<typename _Tp> inline
bool Rect_<_Tp>::contains(const Point_<_Tp>& pt) const
{
    return x <= pt.x && pt.x < x + width && y <= pt.y && pt.y < y + height;
}


template<typename _Tp> static inline
Rect_<_Tp>& operator += ( Rect_<_Tp>& a, const Point_<_Tp>& b )
{
    a.x += b.x;
    a.y += b.y;
    return a;
}

template<typename _Tp> static inline
Rect_<_Tp>& operator -= ( Rect_<_Tp>& a, const Point_<_Tp>& b )
{
    a.x -= b.x;
    a.y -= b.y;
    return a;
}

template<typename _Tp> static inline
Rect_<_Tp>& operator += ( Rect_<_Tp>& a, const Size_<_Tp>& b )
{
    a.width += b.width;
    a.height += b.height;
    return a;
}

template<typename _Tp> static inline
Rect_<_Tp>& operator -= ( Rect_<_Tp>& a, const Size_<_Tp>& b )
{
    a.width -= b.width;
    a.height -= b.height;
    return a;
}

template<typename _Tp> static inline
Rect_<_Tp>& operator &= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
{
    _Tp x1 = std::max(a.x, b.x);
    _Tp y1 = std::max(a.y, b.y);
    a.width = std::min(a.x + a.width, b.x + b.width) - x1;
    a.height = std::min(a.y + a.height, b.y + b.height) - y1;
    a.x = x1;
    a.y = y1;
    if( a.width <= 0 || a.height <= 0 )
        a = Rect();
    return a;
}

template<typename _Tp> static inline
Rect_<_Tp>& operator |= ( Rect_<_Tp>& a, const Rect_<_Tp>& b )
{
    _Tp x1 = std::min(a.x, b.x);
    _Tp y1 = std::min(a.y, b.y);
    a.width = std::max(a.x + a.width, b.x + b.width) - x1;
    a.height = std::max(a.y + a.height, b.y + b.height) - y1;
    a.x = x1;
    a.y = y1;
    return a;
}

template<typename _Tp> static inline
bool operator == (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    return a.x == b.x && a.y == b.y && a.width == b.width && a.height == b.height;
}

template<typename _Tp> static inline
bool operator != (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    return a.x != b.x || a.y != b.y || a.width != b.width || a.height != b.height;
}

template<typename _Tp> static inline
Rect_<_Tp> operator + (const Rect_<_Tp>& a, const Point_<_Tp>& b)
{
    return Rect_<_Tp>( a.x + b.x, a.y + b.y, a.width, a.height );
}

template<typename _Tp> static inline
Rect_<_Tp> operator - (const Rect_<_Tp>& a, const Point_<_Tp>& b)
{
    return Rect_<_Tp>( a.x - b.x, a.y - b.y, a.width, a.height );
}

template<typename _Tp> static inline
Rect_<_Tp> operator + (const Rect_<_Tp>& a, const Size_<_Tp>& b)
{
    return Rect_<_Tp>( a.x, a.y, a.width + b.width, a.height + b.height );
}

template<typename _Tp> static inline
Rect_<_Tp> operator & (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    Rect_<_Tp> c = a;
    return c &= b;
}

template<typename _Tp> static inline
Rect_<_Tp> operator | (const Rect_<_Tp>& a, const Rect_<_Tp>& b)
{
    Rect_<_Tp> c = a;
    return c |= b;
}



////////////////////////////// RotatedRect //////////////////////////////

inline
RotatedRect::RotatedRect()
    : center(), size(), angle(0) {}

inline
RotatedRect::RotatedRect(const Point2f& _center, const Size2f& _size, float _angle)
    : center(_center), size(_size), angle(_angle) {}



///////////////////////////////// Range /////////////////////////////////

inline
Range::Range()
    : start(0), end(0) {}

inline
Range::Range(int _start, int _end)
    : start(_start), end(_end) {}

inline
int Range::size() const
{
    return end - start;
}

inline
bool Range::empty() const
{
    return start == end;
}

inline
Range Range::all()
{
    return Range(INT_MIN, INT_MAX);
}


static inline
bool operator == (const Range& r1, const Range& r2)
{
    return r1.start == r2.start && r1.end == r2.end;
}

static inline
bool operator != (const Range& r1, const Range& r2)
{
    return !(r1 == r2);
}

static inline
bool operator !(const Range& r)
{
    return r.start == r.end;
}

static inline
Range operator & (const Range& r1, const Range& r2)
{
    Range r(std::max(r1.start, r2.start), std::min(r1.end, r2.end));
    r.end = std::max(r.end, r.start);
    return r;
}

static inline
Range& operator &= (Range& r1, const Range& r2)
{
    r1 = r1 & r2;
    return r1;
}

static inline
Range operator + (const Range& r1, int delta)
{
    return Range(r1.start + delta, r1.end + delta);
}

static inline
Range operator + (int delta, const Range& r1)
{
    return Range(r1.start + delta, r1.end + delta);
}

static inline
Range operator - (const Range& r1, int delta)
{
    return r1 + (-delta);
}



///////////////////////////////// Scalar ////////////////////////////////

template<typename _Tp> inline
Scalar_<_Tp>::Scalar_()
{
    this->val[0] = this->val[1] = this->val[2] = this->val[3] = 0;
}

template<typename _Tp> inline
Scalar_<_Tp>::Scalar_(_Tp v0, _Tp v1, _Tp v2, _Tp v3)
{
    this->val[0] = v0;
    this->val[1] = v1;
    this->val[2] = v2;
    this->val[3] = v3;
}

template<typename _Tp> template<typename _Tp2, int cn> inline
Scalar_<_Tp>::Scalar_(const Vec<_Tp2, cn>& v)
{
    int i;
    for( i = 0; i < (cn < 4 ? cn : 4); i++ )
        this->val[i] = cv::saturate_cast<_Tp>(v.val[i]);
    for( ; i < 4; i++ )
        this->val[i] = 0;
}

template<typename _Tp> inline
Scalar_<_Tp>::Scalar_(_Tp v0)
{
    this->val[0] = v0;
    this->val[1] = this->val[2] = this->val[3] = 0;
}

template<typename _Tp> inline
Scalar_<_Tp> Scalar_<_Tp>::all(_Tp v0)
{
    return Scalar_<_Tp>(v0, v0, v0, v0);
}


template<typename _Tp> inline
Scalar_<_Tp> Scalar_<_Tp>::mul(const Scalar_<_Tp>& a, double scale ) const
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(this->val[0] * a.val[0] * scale),
                        saturate_cast<_Tp>(this->val[1] * a.val[1] * scale),
                        saturate_cast<_Tp>(this->val[2] * a.val[2] * scale),
                        saturate_cast<_Tp>(this->val[3] * a.val[3] * scale));
}

template<typename _Tp> inline
Scalar_<_Tp> Scalar_<_Tp>::conj() const
{
    return Scalar_<_Tp>(saturate_cast<_Tp>( this->val[0]),
                        saturate_cast<_Tp>(-this->val[1]),
                        saturate_cast<_Tp>(-this->val[2]),
                        saturate_cast<_Tp>(-this->val[3]));
}

template<typename _Tp> inline
bool Scalar_<_Tp>::isReal() const
{
    return this->val[1] == 0 && this->val[2] == 0 && this->val[3] == 0;
}


template<typename _Tp> template<typename T2> inline
Scalar_<_Tp>::operator Scalar_<T2>() const
{
    return Scalar_<T2>(saturate_cast<T2>(this->val[0]),
                       saturate_cast<T2>(this->val[1]),
                       saturate_cast<T2>(this->val[2]),
                       saturate_cast<T2>(this->val[3]));
}


template<typename _Tp> static inline
Scalar_<_Tp>& operator += (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a.val[0] += b.val[0];
    a.val[1] += b.val[1];
    a.val[2] += b.val[2];
    a.val[3] += b.val[3];
    return a;
}

template<typename _Tp> static inline
Scalar_<_Tp>& operator -= (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a.val[0] -= b.val[0];
    a.val[1] -= b.val[1];
    a.val[2] -= b.val[2];
    a.val[3] -= b.val[3];
    return a;
}

template<typename _Tp> static inline
Scalar_<_Tp>& operator *= ( Scalar_<_Tp>& a, _Tp v )
{
    a.val[0] *= v;
    a.val[1] *= v;
    a.val[2] *= v;
    a.val[3] *= v;
    return a;
}

template<typename _Tp> static inline
bool operator == ( const Scalar_<_Tp>& a, const Scalar_<_Tp>& b )
{
    return a.val[0] == b.val[0] && a.val[1] == b.val[1] &&
           a.val[2] == b.val[2] && a.val[3] == b.val[3];
}

template<typename _Tp> static inline
bool operator != ( const Scalar_<_Tp>& a, const Scalar_<_Tp>& b )
{
    return a.val[0] != b.val[0] || a.val[1] != b.val[1] ||
           a.val[2] != b.val[2] || a.val[3] != b.val[3];
}

template<typename _Tp> static inline
Scalar_<_Tp> operator + (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return Scalar_<_Tp>(a.val[0] + b.val[0],
                        a.val[1] + b.val[1],
                        a.val[2] + b.val[2],
                        a.val[3] + b.val[3]);
}

template<typename _Tp> static inline
Scalar_<_Tp> operator - (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a.val[0] - b.val[0]),
                        saturate_cast<_Tp>(a.val[1] - b.val[1]),
                        saturate_cast<_Tp>(a.val[2] - b.val[2]),
                        saturate_cast<_Tp>(a.val[3] - b.val[3]));
}

template<typename _Tp> static inline
Scalar_<_Tp> operator * (const Scalar_<_Tp>& a, _Tp alpha)
{
    return Scalar_<_Tp>(a.val[0] * alpha,
                        a.val[1] * alpha,
                        a.val[2] * alpha,
                        a.val[3] * alpha);
}

template<typename _Tp> static inline
Scalar_<_Tp> operator * (_Tp alpha, const Scalar_<_Tp>& a)
{
    return a*alpha;
}

template<typename _Tp> static inline
Scalar_<_Tp> operator - (const Scalar_<_Tp>& a)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(-a.val[0]),
                        saturate_cast<_Tp>(-a.val[1]),
                        saturate_cast<_Tp>(-a.val[2]),
                        saturate_cast<_Tp>(-a.val[3]));
}


template<typename _Tp> static inline
Scalar_<_Tp> operator * (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return Scalar_<_Tp>(saturate_cast<_Tp>(a[0]*b[0] - a[1]*b[1] - a[2]*b[2] - a[3]*b[3]),
                        saturate_cast<_Tp>(a[0]*b[1] + a[1]*b[0] + a[2]*b[3] - a[3]*b[2]),
                        saturate_cast<_Tp>(a[0]*b[2] - a[1]*b[3] + a[2]*b[0] + a[3]*b[1]),
                        saturate_cast<_Tp>(a[0]*b[3] + a[1]*b[2] - a[2]*b[1] + a[3]*b[0]));
}

template<typename _Tp> static inline
Scalar_<_Tp>& operator *= (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a = a * b;
    return a;
}

template<typename _Tp> static inline
Scalar_<_Tp> operator / (const Scalar_<_Tp>& a, _Tp alpha)
{
    return Scalar_<_Tp>(a.val[0] / alpha,
                        a.val[1] / alpha,
                        a.val[2] / alpha,
                        a.val[3] / alpha);
}

template<typename _Tp> static inline
Scalar_<float> operator / (const Scalar_<float>& a, float alpha)
{
    float s = 1 / alpha;
    return Scalar_<float>(a.val[0] * s, a.val[1] * s, a.val[2] * s, a.val[3] * s);
}

template<typename _Tp> static inline
Scalar_<double> operator / (const Scalar_<double>& a, double alpha)
{
    double s = 1 / alpha;
    return Scalar_<double>(a.val[0] * s, a.val[1] * s, a.val[2] * s, a.val[3] * s);
}

template<typename _Tp> static inline
Scalar_<_Tp>& operator /= (Scalar_<_Tp>& a, _Tp alpha)
{
    a = a / alpha;
    return a;
}

template<typename _Tp> static inline
Scalar_<_Tp> operator / (_Tp a, const Scalar_<_Tp>& b)
{
    _Tp s = a / (b[0]*b[0] + b[1]*b[1] + b[2]*b[2] + b[3]*b[3]);
    return b.conj() * s;
}

template<typename _Tp> static inline
Scalar_<_Tp> operator / (const Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    return a * ((_Tp)1 / b);
}

template<typename _Tp> static inline
Scalar_<_Tp>& operator /= (Scalar_<_Tp>& a, const Scalar_<_Tp>& b)
{
    a = a / b;
    return a;
}

template<typename _Tp> static inline
Scalar operator * (const Matx<_Tp, 4, 4>& a, const Scalar& b)
{
    Matx<double, 4, 1> c((Matx<double, 4, 4>)a, b, Matx_MatMulOp());
    return reinterpret_cast<const Scalar&>(c);
}

template<> inline
Scalar operator * (const Matx<double, 4, 4>& a, const Scalar& b)
{
    Matx<double, 4, 1> c(a, b, Matx_MatMulOp());
    return reinterpret_cast<const Scalar&>(c);
}



//////////////////////////////// KeyPoint ///////////////////////////////

inline
KeyPoint::KeyPoint()
    : pt(0,0), size(0), angle(-1), response(0), octave(0), class_id(-1) {}

inline
KeyPoint::KeyPoint(Point2f _pt, float _size, float _angle, float _response, int _octave, int _class_id)
    : pt(_pt), size(_size), angle(_angle), response(_response), octave(_octave), class_id(_class_id) {}

inline
KeyPoint::KeyPoint(float x, float y, float _size, float _angle, float _response, int _octave, int _class_id)
    : pt(x, y), size(_size), angle(_angle), response(_response), octave(_octave), class_id(_class_id) {}



///////////////////////////////// DMatch ////////////////////////////////

inline
DMatch::DMatch()
    : queryIdx(-1), trainIdx(-1), imgIdx(-1), distance(FLT_MAX) {}

inline
DMatch::DMatch(int _queryIdx, int _trainIdx, float _distance)
    : queryIdx(_queryIdx), trainIdx(_trainIdx), imgIdx(-1), distance(_distance) {}

inline
DMatch::DMatch(int _queryIdx, int _trainIdx, int _imgIdx, float _distance)
    : queryIdx(_queryIdx), trainIdx(_trainIdx), imgIdx(_imgIdx), distance(_distance) {}

inline
bool DMatch::operator < (const DMatch &m) const
{
    return distance < m.distance;
}



////////////////////////////// TermCriteria /////////////////////////////

inline
TermCriteria::TermCriteria()
    : type(0), maxCount(0), epsilon(0) {}

inline
TermCriteria::TermCriteria(int _type, int _maxCount, double _epsilon)
    : type(_type), maxCount(_maxCount), epsilon(_epsilon) {}

//! @endcond

} // cv

#endif //__OPENCV_CORE_TYPES_HPP__