2-D Variance

Compute variance of input or sequence of inputs

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Libraries:
Computer Vision Toolbox / Statistics

Description

The 2-D Variance block computes the unbiased variance of an input array. The input can be a 1-D vector, 2-D matrix, or an N-D array. The block can compute variance along a specified dimension of the input or the entire input. If you select the Running variance parameter, the block can also track the variance in a sequence of inputs over a time period.

Examples

Compute Variance of ROIs

Compute the variance of regions of interest (ROIs) in the input image. The input image consists of different texture regions, and a mask image specifies ROIs selected to contain the texture regions.

• Open Live Script

Ports

Input

In — Input array

vector | matrix | array

Input array, specified as a vector, matrix, or N-D- array. This port is unnamed until you select the Enable ROI processing parameter.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point
Complex Number Support: Yes

Rst — Reset port

scalar

Reset port, specified as a scalar. This port specifies the event that causes the block to reset the running variance. The sample time of the Rst input must be a positive integer and a multiple of the input sample time.

Dependencies

To enable this port, select the Running variance parameter and set the Reset port parameter to Rising edge, Falling edge, Either edge, or Non-zero sample.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean

ROI — Region of interest

vector | matrix

Region of interest (ROI), specified as a four-element vector, m-by-4 matrix, or M-by-N matrix. The input value to this port depends on the ROI type parameter.

Note

You can use the ROI port only if the input is a 2-D image.

Dependencies

To enable this port, set the Find the variance value over parameter to Entire input and select the Enable ROI processing parameter.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | Boolean | fixed point

Label — Label matrix

matrix

Label matrix, specified as a matrix of nonnegative integers. The label matrix represents the objects in an image. The pixels labeled 0 are the background. The pixels labeled 1 make up one object; the pixels labeled 2 make up a second object; and so on. The size of the label matrix must be the same size as the 2-D input.

Dependencies

To enable this port, select the Enable ROI processing parameter and set the ROI type parameter to Label matrix.

Data Types: uint8 | uint16 | uint32

Label Numbers — Label values of ROIs

vector

Label values of ROIs, specified as a M-element vector. The value of M can be less than or equal to the number of objects that are labeled in the label matrix.

Dependencies

To enable this port, select the Enable ROI processing parameter and set the ROI type parameter to Label matrix.

Data Types: uint8 | uint16 | uint32

Output

Out — Computed output variance

scalar | vector | matrix | N-D-array

Computed output variance, returned as a scalar, vector, matrix, or N-D-array. The size of the returned output variance depends on the size of the input, and the settings for the Running variance and Find the variance value over parameters.

This port is unnamed until you select the Output flag indicating if ROI is within image bounds and the ROI type parameter is set to Rectangles, Lines, or Label matrix.

If Running variance Is Cleared

You can compute variance along any specified dimension of the input or the entire input. The output is a:

• Scalar if the input is of any size and the Find the variance value over parameter is set to Entire input.

• Vector if the input is a matrix and the Find the variance value over parameter is set to any one of Each row, Each column, and Specified dimension. In this case, the Dimension value for Specified dimension can be either 1 or 2.

• Matrix if the input is a 3-D array and the Find the variance value over parameter is set to Specified dimension and the Dimension value is 3.

• N-D array if the input is an N-D array and the Find the variance value over parameter is set to an option other than Entire input.

  If you compute variance along the Nth dimension of the input, then the returned output is an (N-1)-D array. In this case, the Dimension value for Specified dimension is set to N.

  Example: For a 3-D input array of size M-by-N-by-P, the dimension of the returned output is:

  • 1-by-N-by-P if you set the Find the variance value over parameter to Entire row.

  • M-by-1-by-P if you set the Find the variance value over parameter to Entire column.

  • M-by-N if you set the Find the variance value over parameter to Specified dimension and the Dimension value to 3.

If Running variance Is Selected

When you select the Running variance parameter, the block computes the variance of each sample in the input with respect to all previous samples. The output is of the same size as the input.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32 | fixed point

Flag — Validation for ROI

0 | 1

Validation for ROI, returned as 0 or 1. The output value signifies if all of the ROIs specified at the input lie within the image bounds. The output value depends on the values of the Output and ROI Type parameters.

ROI Type	Output	Output from Flag port	Description
Rectangles Lines	Individual statistics for each ROI	0	ROI is completely outside the input image.
		1	ROI is either completely or partially inside the input image.
	Single statistic for all ROIs	0	ROI is completely outside the input image.
		1	ROI is either completely or partially inside the input image.
Label matrix	Individual statistics for each ROI	0	Label number is not in the label matrix.
		1	Label number is in the label matrix.
	Single statistic for all ROIs	0	None of the label numbers are in the label matrix.
		1	At least one of the label numbers is in the label matrix.

Note

If the ROI is partially outside the image, the block computes the variance values only for the portion of the ROI that lies within the image bounds.

Dependencies

To enable this port, select the Output flag indicating if ROI is within image bounds parameter and set the value of ROI type parameter to Rectangle, Lines, or Label Matrix.

Parameters

Main

Running variance — Track running variance

off (default) | on

Select to track the variance of successive inputs to the block. In this mode, the block treats each element as a channel.

Reset port — Reset event

None (default) | Rising edge | Falling edge | Either edge | Non-zero sample

Specify when the block detects a reset event. The block resets the running variance when a reset event is detected at the optional Rst port. The reset sample time must be a positive integer and a multiple of the input sample time.

Specify the reset event as:

• None to disable the Rst port.

• Rising edge to trigger a reset event when the Rst input does one of the following:

  • Rises from a negative value to either a positive value or zero

  • Rises from zero to a positive value, where the rise is not a continuation of a rise from a negative value to zero

    

• Falling edge to trigger a reset event when the Rst input does one of the following:

  • Falls from a positive value to either a negative value or zero

  • Falls from zero to a negative value, where the fall is not a continuation of a fall from a positive value to zero

    

• Either edge to trigger a reset event when the Rst input is a Rising edge or Falling edge.

• Non-zero sample to trigger a reset event at each sample time, when the Rst input is not zero.

  Note

  When running simulations in the Simulink^® multitasking mode, reset signals have a one-sample latency. Therefore, when the block detects a reset event, there is a one-sample delay at the reset port rate before the block applies the reset.

Dependencies

To enable this parameter, select the Running variance parameter.

Find the variance value over — Dimension along which variance is computed

Entire input (default) | Each row | Each column | Specified dimension

Specify the dimension of the input along which the block computes the variance.

• Entire input — Computes variance over the entire input.

• Each row — Computes variance over each row.

• Each column — Computes variance over each column.

• Specified dimension— Computes variance over the dimension specified in the Dimension parameter.

  • If Dimension is 1, the output is the same as when you select Each column.

  • If Dimension is 2, the output is the same as when you select Each row.

Dependencies

To enable this parameter, clear the Running variance parameter.

Dimension — Custom dimension

1 (default) | scalar

Specify the dimension of the input array over which the variance is computed as a one-based value. The value of this parameter must be greater than 0 and less than or equal to the number of dimensions in the input array.

Dependencies

To enable this parameter, set the Find the variance value over parameter to Specified dimension.

ROI Processing

Enable ROI processing — Compute variance within a particular region

off (default) | on

Select to calculate variance within a particular ROI in the image.

Note

Full ROI processing is available only if you have a Computer Vision Toolbox™ license. If you do not have a Computer Vision Toolbox license, you can still use ROI processing, but the ROI type is limited to Rectangles.

Dependencies

To enable this parameter, set the Find the variance value over parameter to Entire input.

ROI type — Type of ROI

Rectangles (default) | Lines | Label matrix | Binary mask

Specify the type of ROI that represents the regions in the image over which the block computes the variance. The type of ROI can be a rectangle, line, label matrix, or a binary mask.

Parameters		Description
ROI type	Inputs to the ROI port
Rectangles	Four-element row vector [x y width height] m-by-4 matrix $$\left[\begin{array}{cccc}{x}_1& y_1& widt{h}_1& heigh{t}_1\\ x_2& y_2& widt{h}_2& heigh{t}_2\\ ⋮& ⋮& ⋮& ⋮\\ x_M& y_M& widt{h}_M& heigh{t}_M\end{array}\right]$$ , where m is the number of rectangles. Each row of the matrix corresponds to a different rectangle.	x and y are the one-based coordinates of the upper left corner of the rectangle. width and height are the width and height, in pixels, of the rectangle. The values of width and height must be greater than 0.
Lines	Four-element row vector [x1 y1 x2 y2] m-by-4 matrix $$\left[\begin{array}{cccc}{x}_{11}& y_{11}& x_{12}& y_{12}\\ x_{21}& y_{21}& x_{22}& y_{22}\\ ⋮& ⋮& ⋮& ⋮\\ x_{M1}& y_{M1}& x_{M2}& y_{M2}\end{array}\right]$$ , where m is the number of lines. Each row of the matrix corresponds to a different line.	x1 and y1 are the coordinates of the beginning of the line. x2 and y2 are the coordinates of the end of the line.
Label matrix	M-by-N matrix	Matrix of the same size as the input image. The matrix contains label values that represent different objects in an image. The pixels labeled 0 are the background. The pixels labeled 1 make up one object; the pixels labeled 2 make up a second object; and so on.
Binary mask	M-by-N matrix	Matrix of the same size as the input image. The binary mask classifies image pixels as belonging to either the region of interest or the background. The mask pixel values of 1 indicate that the image pixel belongs to the ROI. The mask pixel values of 0 indicate that the image pixel is part of the background.

Dependencies

To enable this parameter, select the Enable ROI processing parameter.

ROI portion to process — Portion of ROI in which to calculate variance

Entire ROI (default) | ROI perimeter

Specify the portion of the ROI from which the block has to calculate 2-D variance. The ROI portion is either the entire ROI or the ROI perimeter.

Dependencies

To enable this parameter, select the Enable ROI processing parameter and set the ROI type parameter to Rectangles.

Output — Calculate variance for individual or entire ROI

Individual statistics for each ROI (default) | Single statistic for all ROIs

Specify whether to calculate 2-D variance individually for each ROI or for the entire ROI.

• If you select Individual statistics for each ROI, the block outputs a vector of variance values. The size of the output vector is equal to the number of ROIs.

• If you select Single statistic for all ROIs, the block outputs a scalar value. The scalar value represents the statistical value for all the specified ROIs.

Dependencies

To enable this parameter, select the Enable ROI processing parameter and set the ROI type parameter to Rectangles, Lines, or Label matrix.

Output flag indicating if ROI is within image bounds — Enable Flag port

off (default) | on

Select to expose the Flag port. For a description of the Flag port output, see Flag.

Dependencies

To enable this parameter, select the Enable ROI processing parameter and set the ROI type parameter to Rectangles, Lines, or Label matrix.

Data Types

For details on the fixed-point block parameters, see Specify Fixed-Point Attributes for Blocks (DSP System Toolbox).

Lock data type settings against change by the fixed-point tools — Prevent fixed-point tools from overriding data types

off (default) | on

Select this parameter to prevent the fixed-point tools from overriding the data types you specify in this block. For more information, see Lock the Output Data Type Setting (Fixed-Point Designer).

Block Characteristics

Data Types	double | fixed point | integer | single
Multidimensional Signals	yes
Variable-Size Signals	yes

More About

Variance

The variance of an input is the square of the standard deviation of the input. Variance gives a measure of deviation of the input values from its mean value.

For a purely real or imaginary input, u, of size M-by-N, the variance is:

$$y={\sigma }^2=\frac{{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N{\left|u_{ij}\right|}^2-\frac{{\left|{\displaystyle \sum _{i=1}^M{\displaystyle \sum _{j=1}^N{u}_{ij}}}\right|}^2}{M*N}}}}{M*N-1},$$

where:

• u_ij is the input data element at (i, j).

• M is the length of the jth column.

• N is the number of columns.

For complex inputs, the variance is:

$${\sigma }^2={\sigma }_{\mathrm{Re}}{}^2+{\sigma }_{\mathrm{Im}}{}^2,$$

where:

• σ_Re² is the variance of the real part of the complex input.

• σ_Im² is the variance of the imaginary part of the complex input.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced before R2006a