Functions
I32	rlc_moments (U16 r0, moment mx, U32 n)
	Calculate Moments of Order 0, 1, 2 for Labelled RLC. More...

I32	rlc_moments3 (U16 rl0, moment mq, U32 n)
	Calculate Moments of Order 0, 1, 2 and 3 for Labelled RLC. More...

F32	mom_calc_area (moment *mx)
	Calculate Area from Moments. More...

F32	mom_calc_cgx (moment *mx)
	Calculate Center of Gravity X-Coordinate from Moments. More...

F32	mom_calc_cgy (moment *mx)
	Calculate Center of Gravity Y-Coordinate from Moments. More...

F32	mom_calc_angle (moment *mx)
	Calculate Angle of Inertial Axis from Moments (Result in Degrees). More...

F32	mom_calc_rad (moment *mx)
	Calculate Angle of Inertial Axis from Moments (Result in Radiants). More...

F32	mom_calc_ecc (moment *mx)
	Calculate Object Eccentricity from Moments. More...

F32	mom_calc_ellipse_a (moment *mx)
	Calculate Ellipse Half-Parameters. More...

F32	mom_calc_ellipse_b (moment *mx)
	Calculate Ellipse Half-Parameters. More...

F32	mom_calc_phi1 (moment *mx)
	Calculate Hu Moments. More...

F32	mom_calc_phi2 (moment *mx)
	Calculate Hu Moments. More...

F32	mom_calc_phi3 (moment *mx)
	Calculate Third Hu Moment. More...

F32	mom_calc_phi4 (moment *mx)
	Calculate Fourth Hu Moment. More...

F32	mom_calc_ai1 (moment *mx)
	Calculate Affine Invariant Moment 1. More...

F32	mom_calc_ai2 (moment *mx)
	Calculate Affine Invariant Moment 2. More...

F32	mom_calc_ai3 (moment *mx)
	Calculate Affine Invariant Moment 3. More...

Detailed Description

For a description see the section Moments.

Function Documentation

◆ rlc_moments()

I32 rlc_moments	(	U16 *	rl0,
		moment *	mq,
		U32	n
	)

The function calculates the centralized moments of order 0, 1 and 2 for the labelled runlength code rlc. The centralized moments may be used to calculate useful features present in the RLC. For example the moment $\mu_{0,0}$ is equal to the total pixel area of the object. With moments $\mu_{1,0}$ and $\mu_{0,1}$ , the center of gravity for the object can be calculated by dividing these values by $\mu_{0,0}$ . Higher moments may be used to calculate translation-, rotation- and scaling-invariant object features. The output of the function is stored in the struct array mom. All values of this struct are stored in our proprietary multi-precision integer format. Since there are additional functions available to calculate all meaningful features, it is not necessary to use these values directly. The definition of the moment struct:

typedef struct   // centralized moments 
{ BITN mu00;     // order 0             
  BITN mu10;     // order 1             
  BITN mu01;     // order 1             
  BITN mu20;     // order 2             
  BITN mu11;     // order 2             
  BITN mu02;     // order 2             
  BITN mu30;     // order 3             
  BITN mu21;     // order 3             
  BITN mu12;     // order 3             
  BITN mu03;     // order 3             
} moment;

Moments of order 3 in this struct are not written with this function. The function rlc_moments() only calculates moments up to the second order. Moments of order 3 can be calculated using function rlc_moments3(). Please refer to Gonzalez, Wintz: "Digital Image Processing", Addison-Wesley 1977 pp. 354ff for the definition of the moments.

Input variables for the function:

Parameters

rl0	Pointer to Labelled RLC (Input to the Function).
mq	Array of Struct (Moment Struct) / Function Output.
n	Number of Array Elements in `mom`. The function checks wether this number is sufficiently high for all objects in the RLC. If not, the function returns with an error code.

On success, the function returns the number of objects in the RLC. This value may be used to address the output struct array. The standard error code is returned on error: RLC is unlabelled or it contains more objects than n.

Memory Consumption: nobj * (tbd) Bytes of Heap Memory.

See also: rlc_moments3(), mom_calc_cgx(), mom_calc_cgy(), mom_calc_angle(), mom_calc_ecc(), mom_calc_phi1(), mom_calc_phi2().

Return values

ERR_SLC	if RLC is Unlabelled.
ERR_RLC_ONOVR	if an Object Number Overrun occured.
ERR_RLC_MEM	if Memory Allocation Fails.
Object Count	on Success.

◆ rlc_moments3()

I32 rlc_moments3	(	U16 *	rl0,
		moment *	mq,
		U32	n
	)

The function calculates the centralized moments of order 0 through 3 for the labelled runlength code rlc. The centralized moments may be used to calculate useful features present in the RLC. For example the moment $\mu_{0,0}$ is equal to the total pixel area of the object. With moments $\mu_{1,0}$ and $\mu_{0,1}$ , the center of gravity for the object can be calculated by dividing these values by $\mu_{0,0}$ . Higher moments may be used to calculate translation-, rotation-, scaling- and even affine-invariant object features. The output of the function is stored in the struct array mom. All values of this struct are stored in our proprietary multi-precision integer format. Since there are additional functions available to calculate all meaningful features, it is not necessary to use these values directly. The definition of the moment struct:

typedef struct   // centralized moments
{ BITN mu00;     // order 0
  BITN mu10;     // order 1
  BITN mu01;     // order 1
  BITN mu20;     // order 2
  BITN mu11;     // order 2
  BITN mu02;     // order 2
  BITN mu30;     // order 3
  BITN mu21;     // order 3
  BITN mu12;     // order 3
  BITN mu03;     // order 3
} moment;

The function rlc_moments3() calculates moments up to the third order. Please refer to Gonzalez, Wintz: "Digital Image Processing", Addison-Wesley 1977 pp. 354ff for the definition of the moments.

Input variables for the function:

Parameters

rl0	Pointer to Labelled RLC (Input to the Function).
mq	Array of Struct (Moment Struct) / Function Output.
n	Number of Array Elements in `mom`. The function checks whether this number is sufficiently high for all objects in the RLC. If not, the function returns with an error code.

On success, the function returns the number of objects in the RLC. This value may be used to address the output struct array. The standard error code is returned on error: RLC is unlabelled or it contains more objects than n.

Memory Consumption: nobj * (tbd) Bytes of Heap Memory.

See also: rlc_moments3(), mom_calc_cgx(), mom_calc_cgy(), mom_calc_angle(), mom_calc_ecc(), mom_calc_phi1(), mom_calc_phi2(), (), (), (), ().

Return values

ERR_SLC	if RLC is Unlabelled.
ERR_RLC_ONOVR	if an Object Number Overrun occured.
ERR_RLC_MEM	if Memory Allocation Fails.
Object Count	on Success.

◆ mom_calc_area()

F32 mom_calc_area ( moment * mx )

The function mom_calc_area() returns the pixel count of the object.

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_cgx()

F32 mom_calc_cgx ( moment * mx )

The functions mom_calc_cgx() and mom_calc_cgy() compute the x- and y-coordinates of the center of gravity for the object with the centralized moments given by mom. The output of the funtion is a float value with subpixel accuracy.

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_cgy()

F32 mom_calc_cgy ( moment * mx )

The functions mom_calc_cgx() and mom_calc_cgy() compute the x- and y-coordinates of the center of gravity for the object with the centralized moments given by mom. The output of the funtion is a float value with subpixel accuracy.

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_angle()

F32 mom_calc_angle ( moment * mx )

The function computes the angle of the inertial axis (minimum moment of inertia) for the object with the centralized moments given by mom. This may be used as the main object orientation, e.g. for robot applications. The output of the function is a float value with subangle accuracy ranging from 0.0 to 179.9 degrees. A value of 0 means, that the object is oriented parallel to the (horizontal) x-axis, '90' means it is parallel to the y-axis. The user must be careful: Since the output does not cover the full range from 0 to 360 degrees, it is not possible to differentiate mirrored positions of the object. The function is also useless for objects with circular symmetry, e.g. for disks, squares and the like. Use the function mom_calc_ecc() to see if the object has some kind of eccentricity which is necessary for a unique inertial axis.

Memory Consumption: None.

See also: rlc_moments(), mom_calc_rad().

◆ mom_calc_rad()

F32 mom_calc_rad ( moment * mx )

The function computes the angle of the inertial axis (minimum moment of inertia) for the object with the centralized moments given by mom. This may be used as the main object orientation, e.g. for robot applications. The output of the funtion is a float value with subangle accuracy ranging from 0.0 to π. 0 means, the object is oriented parallel to the (horizontal) x-axis, π/2 means it is parallel to the y-axis. The user must be careful: Since the output does not cover the full range from 0 to 2π, it is not possible to differentiate mirrored positions of the object. The function is also useless for objects with circular symmetry, e.g. for disks, squares and the like. Use the function mom_calc_ecc(), to see if the object has some kind of eccenticity which is necessary for a unique inertial axis.

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_ecc()

F32 mom_calc_ecc ( moment * mx )

The function computes the eccentricity for the object with the centralized moments given by mom. This may be used as the main object orientation, e.g. for robot applications. The output of the funtion is a float value with ranging from 0.0 to 1.0. '0.0' means, the object is totally symmetric, like a disk or a square, '1.0' means the object is totally eccentric, like a needle. The eccentricity for an ellipsoid with half-diameter a and b, the eccentricity would be (a - b)/(a + b).

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_ellipse_a()

F32 mom_calc_ellipse_a ( moment * mx )

The functions mom_calc_ellipse_a() and mom_calc_ellipse_b() calculate the half-parameters a and b of the equivalent ellipse for the object with the centralized moments given by mom.

Memory Consumption: None.

See also: rlc_moments(), mom_calc_ecc().

◆ mom_calc_ellipse_b()

F32 mom_calc_ellipse_b ( moment * mx )

The functions mom_calc_ellipse_a() and mom_calc_ellipse_b() calculate the half-parameters a and b of the equivalent ellipse for the object with the centralized moments given by mom.

Memory Consumption: None.

See also: rlc_moments(), mom_calc_ecc().

◆ mom_calc_phi1()

F32 mom_calc_phi1 ( moment * mx )

The functions mom_calc_phi1() and mom_calc_phi2() compute the first two Hu moments.

With the definition:

$\begin{eqnarray*} \eta_{2,0} &=& \mu_{2,0} / \mu_{0,0}^2 \\ \eta_{1,1} &=& \mu_{1,1} / \mu_{0,0}^2 \\ \eta_{0,2} &=& \mu_{0,2} / \mu_{0,0}^2 \\ \end{eqnarray*}$

the first two Hu moments are defined as follows:

$\begin{eqnarray*} \varphi_1 &=& \eta_{2,0} + \eta_{0,2} \\ \varphi_2 &=& (\eta_{2,0} - \eta_{0,2})^2 + 4*\eta_{1,1}^2 \\ \end{eqnarray*}$

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_phi2()

F32 mom_calc_phi2 ( moment * mx )

The functions mom_calc_phi1() and mom_calc_phi2() compute the first two Hu moments.

With the definition:

$\begin{eqnarray*} \eta_{2,0} &=& \mu_{2,0} / \mu_{0,0}^2 \\ \eta_{1,1} &=& \mu_{1,1} / \mu_{0,0}^2 \\ \eta_{0,2} &=& \mu_{0,2} / \mu_{0,0}^2 \\ \end{eqnarray*}$

the first two Hu moments are defined as follows:

$\begin{eqnarray*} \varphi_1 &=& \eta_{2,0} + \eta_{0,2} \\ \varphi_2 &=& (\eta_{2,0} - \eta_{0,2})^2 + 4*\eta_{1,1}^2 \\ \end{eqnarray*}$

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_phi3()

F32 mom_calc_phi3 ( moment * mx )

The function computes the third Hu moment.

With the definition:

$\begin{eqnarray*} \eta_{2,0} &=& \mu_{2,0} / \mu_{0,0}^2 \\ \eta_{1,1} &=& \mu_{1,1} / \mu_{0,0}^2 \\ \eta_{0,2} &=& \mu_{0,2} / \mu_{0,0}^2 \\ \end{eqnarray*}$

the third Hu moment is defined as follows:

$\begin{eqnarray*} \varphi_3 &=& (\eta_{3,0} - 3*\eta_{1,2})^2 + (3*\eta_{2,1} - \eta_{0,3})^2 \\ \end{eqnarray*}$

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_phi4()

F32 mom_calc_phi4 ( moment * mx )

The function computes the fourth Hu moment.

With the definition:

$\begin{eqnarray*} \eta_{2,0} &=& \mu_{2,0} / \mu_{0,0}^2 \\ \eta_{1,1} &=& \mu_{1,1} / \mu_{0,0}^2 \\ \eta_{0,2} &=& \mu_{0,2} / \mu_{0,0}^2 \\ \end{eqnarray*}$

the fourth Hu moment is defined as follows:

$\begin{eqnarray*} \varphi_4 &=& (\eta_{3,0} + \eta_{1,2})^2 + (\eta_{2,1} + \eta_{0,3})^2 \\ \end{eqnarray*}$

Memory Consumption: None.

See also: rlc_moments().

◆ mom_calc_ai1()

F32 mom_calc_ai1 ( moment * mx )

The function computes the first Affine Invariant Moment.

With the definition:

$\begin{eqnarray*} \eta_{2,0} &=& \mu_{2,0} / \mu_{0,0}^2 \\ \eta_{1,1} &=& \mu_{1,1} / \mu_{0,0}^2 \\ \eta_{0,2} &=& \mu_{0,2} / \mu_{0,0}^2 \\ \end{eqnarray*}$

the first Affine Invariant Moment is defined as follows:

$\begin{eqnarray*} \varphi_2 &=& \over{((\eta_{2,0} * \eta_{0,2}) - \eta_{1,1}^2)}{\eta_{0,0}^4} \\ \end{eqnarray*}$

Affine Invariants are fully explained in Flusser, Suk, Zitova: "Moments and Moment Invariants in Pattern Recognition", Wiley 2009, pp 60 ff.

Memory Consumption: None.

See also: rlc_moments(), mom_calc_phi1().

◆ mom_calc_ai2()

F32 mom_calc_ai2 ( moment * mx )

The function computes the second Affine Invariant Moment.

Affine Invariants are fully explained in Flusser, Suk, Zitova: "Moments and Moment Invariants in Pattern Recognition", Wiley 2009, pp 60 ff.

Memory Consumption: None.

See also: rlc_moments(), mom_calc_phi1().

◆ mom_calc_ai3()

F32 mom_calc_ai3 ( moment * mx )

The function computes the third Affine Invariant Moment.

Affine Invariants are fully explained in Flusser, Suk, Zitova: "Moments and Moment Invariants in Pattern Recognition", Wiley 2009, pp 60 ff.

Memory Consumption: None.

See also: rlc_moments(), mom_calc_phi1().

RLC Moments

Functions

Detailed Description

Function Documentation

◆ rlc_moments()

◆ rlc_moments3()

◆ mom_calc_area()

◆ mom_calc_cgx()

◆ mom_calc_cgy()

◆ mom_calc_angle()

◆ mom_calc_rad()

◆ mom_calc_ecc()

◆ mom_calc_ellipse_a()

◆ mom_calc_ellipse_b()

◆ mom_calc_phi1()

◆ mom_calc_phi2()

◆ mom_calc_phi3()

◆ mom_calc_phi4()

◆ mom_calc_ai1()

◆ mom_calc_ai2()

◆ mom_calc_ai3()