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Minimum - Find minimum values in input or sequence of inputs

Library

Statistics

dspstat3

Description

The Minimum block identifies the value and/or position of the smallest element in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input. The Minimum block can also track the minimum values in a sequence of inputs over a period of time. The Mode parameter specifies the block's mode of operation, and can be set to Value, Index, Value and Index, or Running.

The Minimum block supports real and complex floating-point, fixed-point, and Boolean inputs. Real fixed-point inputs can be either signed or unsigned, while complex fixed-point inputs must be signed. The data type of the minimum values output by the block match the data type of the input. The index values output by the block are double when the input is double, and uint32 otherwise.

The frame status of the block output is the same as that of the input, except when the Find the minimum value of parameter is set to Entire input. The output is always sample-based when Entire input is selected.

For the Value, Index, and Value and Index modes, the Minimum block produces identical results as the MATLAB min function when it is called as [y I] = min(u,[],D), where u and y are the input and output, respectively, D is the dimension, and I is the index.

Value Mode

When the Mode parameter is set to Value, the block computes the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input at each sample time, and outputs the array y. Each element in y is the minimum value in the corresponding column, row, vector, or entire input. The output y depends on the setting of the Find the minimum value over parameter. For example, consider a 3-dimensional input signal of size M-by-N-by-P:

Each row — The output at each sample time consists of an M-by-1-by-P array, where each element contains the minimum value of each vector over the second dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is an M-by-1 column vector. In this mode, the frame status of the output is the same as that of the input.
Each column — The output at each sample time consists of a 1-by-N-by-P array, where each element contains the minimum value of each vector over the first dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is a 1-by-N row vector. In this mode, the frame status of the output is the same as that of the input.
For convenience, length-M 1-D vector inputs are treated as M-by-1 column vectors when the block is in this mode. Sample-based length-M row vector inputs are also treated as M-by-1 column vectors when the Treat sample-based row input as a column check box is selected.
Entire input — The output at each sample time is a scalar that contains the minimum value in the M-by-N-by-P input matrix. In this mode, the block output is always sample based.
Specified dimension — The output at each sample time depends on Dimension. If Dimension is set to 1, the output is the same as when you select Each column. If Dimension is set to 2, the output is the same as when you select Each row. If Dimension is set to 3, the output at each sample time is an M-by-N matrix containing the minimum value of each vector over the third dimension of the input. In this mode, the frame status of the output is the same as that of the input.

For complex inputs, the block selects the value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input that has the minimum magnitude squared as shown below. For complex value , the magnitude squared is .

Index Mode

When Mode is set to Index, the block computes the minimum value in each row or column of the input, along vectors of a specified dimension of the input, or of the entire input, and outputs the index array I. Each element in I is an integer indexing the minimum value in the corresponding column, row, vector, or entire input. The output I depends on the setting of the Find the minimum value over parameter. For example, consider a 3-dimensional input signal of size M-by-N-by-P:

Each row — The output at each sample time consists of an M-by-1-by-P array, where each element contains the index of the minimum value of each vector over the second dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is an M-by-1 column vector. In this mode, the frame status of the output is the same as that of the input.
Each column — The output at each sample time consists of a 1-by-N-by-P array, where each element contains the index of the minimum value of each vector over the first dimension of the input. For an input that is an M-by-N matrix, the output at each sample time is a 1-by-N row vector. In this mode, the frame status of the output is the same as that of the input.
For convenience, length-M 1-D vector inputs are treated as M-by-1 column vectors when the block is in this mode. Sample-based length-M row vector inputs are also treated as M-by-1 column vectors when the Treat sample-based row input as a column check box is selected.
Entire input — The output at each sample time is a 1-by-3 vector that contains the location of the minimum value in the M-by-N-by-P input matrix. In this mode, the block output is always sample based. For an input that is an M-by-N matrix, the output will be a 1-by-2 vector.
Specified dimension — The output at each sample time depends on Dimension. If Dimension is set to 1, the output is the same as when you select Each column. If Dimension is set to 2, the output is the same as when you select Each row. If Dimension is set to 3, the output at each sample time is an M-by-N matrix containing the indices of the minimum values of each vector over the third dimension of the input. In this mode, the frame status of the output is the same as that of the input.

When a minimum value occurs more than once, the computed index corresponds to the first occurrence. For example, when the input is the column vector [-1 2 3 2 -1]', the computed one-based index of the minimum value is 1 rather than 5 when Each column is selected.

Value and Index Mode

When Mode is set to Value and Index, the block outputs both the minima and the indices.

Running Mode

When Mode is set to Running, the block tracks the minimum value of each channel in a time sequence of M-by-N inputs. For sample-based inputs, the output is a sample-based M-by-N array with each element y_ij containing the minimum value observed in element u_ij for all inputs since the last reset. For frame-based inputs, the output is a frame-based M-by-N array with each element y_ij containing the minimum value observed in the jth column of all inputs since the last reset, up to and including element u_ij of the current input.

N-D signals cannot be frame based. When the block is set to Running mode, each element of the N-D signal is considered as a separate channel. There are channels, where d_i is the size of the ith dimension.

Resetting the Running Minimum

The block resets the running minimum whenever a reset event is detected at the optional Rst port. The reset sample time must be a positive integer multiple of the input sample time.

When the block is reset for sample-based inputs, the running minimum for each channel is initialized to the value in the corresponding channel of the current input. For frame-based inputs, the running minimum for each channel is initialized to the earliest value in each channel of the current input.

You specify the reset event by the Reset port parameter:

None — Disables the Rst port
Rising edge — Triggers a reset operation when the Rst input does one of the following:
- Rises from a negative value to 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 (see the following figure)
Falling edge — Triggers a reset operation when the Rst input does one of the following:
- Falls from a positive value to 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 (see the following figure)

Either edge — Triggers a reset operation when the Rst input is a Rising edge or Falling edge (as described above)
Non-zero sample — Triggers a reset operation at each sample time that 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. For more information on latency and the Simulink tasking modes, see Excess Algorithmic Delay (Tasking Latency) and Scheduling Considerations in the Real-Time Workshop User's Guide.

ROI Processing

To calculate the statistical value within a particular region of interest (ROI) of the input, select the Enable ROI processing check box. This option is only available when the Find the minimum value over parameter is set to Entire input and the Enable ROI processing check box is selected. ROI processing is only supported for 2-D inputs.

Note Full ROI processing is only available to users who have a Video and Image Processing Blockset license. If you only have a Signal Processing Blockset license, you can still use ROI processing, but are limited to the ROI type Rectangles.

Use the ROI type parameter to specify whether the ROI is a rectangle, line, label matrix, or binary mask. A binary mask is a binary image that enables you to specify which pixels to highlight, or select. In a label matrix, pixels equal to 0 represent the background, pixels equal to 1 represent the first object, pixels equal to 2 represent the second object, and so on. When the ROI type parameter is set to Label matrix, the Label and Label Numbers ports appear on the block. Use the Label Numbers port to specify the objects in the label matrix for which the block calculates statistics. The input to this port must be a vector of scalar values that correspond to the labeled regions in the label matrix. For more information about the format of the input to the ROI port when the ROI is a rectangle or a line, see the Draw Shapes block reference page.

For rectangular ROIs, use the ROI portion to process parameter to specify whether to calculate the statistical value for the entire ROI or just the ROI perimeter.

Use the Output parameter to specify the block output. The block can output separate statistical values for each ROI or the statistical value for all specified ROIs. This parameter is not available if, for the ROI type parameter, you select Binary mask.

If, for the ROI type parameter, you select Rectangles or Lines, the Output flag indicating if ROI is within image bounds check box appears in the dialog box. If you select this check box, the Flag port appears on the block. The following tables describe the Flag port output based on the block parameters.

Output = Individual statistics for each ROI

Flag Port Output	Description
0	ROI is completely outside the input image.
1	ROI is completely or partially inside the input image.

Output = Single statistic for all ROIs

Flag Port Output	Description
0	All ROIs are completely outside the input image.
1	At least one ROI is completely or partially inside the input image.

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

If, for the ROI type parameter, you select Label matrix, the Output flag indicating if input label numbers are valid check box appears in the dialog box. If you select this check box, the Flag port appears on the block. The following tables describe the Flag port output based on the block parameters.

Output = Individual statistics for each ROI

Flag Port Output	Description
0	Label number is not in the label matrix.
1	Label number is in the label matrix.

Output = Single statistic for all ROIs

Flag Port Output	Description
0	None of the label numbers are in the label matrix.
1	At least one of the label numbers is in the label matrix.

Fixed-Point Data Types

The parameters on the Data type attributes pane of the block dialog are only used for complex fixed-point inputs. The sum of the squares of the real and imaginary parts of such an input are formed before a comparison is made, as described in Value Mode. The results of the squares of the real and imaginary parts are placed into the product output data type. The result of the sum of the squares is placed into the accumulator data type. These parameters are ignored for other types of inputs.

Examples

The Minimum block in the following model calculates the running minimum of a frame-based 3-by-2 (two-channel) matrix input. The running minimum is reset at t=2 by an impulse to the block's Rst port.

The Minimum block has the following settings:

Mode = Running
Reset port = Non-zero sample

The Signal From Workspace block has the following settings:

Signal = u
Sample time = 1/3
Samples per frame = 3

where

u = [6 1 3 -7 2 5 8 0 -1 -3 2 1;1 3 9 2 4 2 6 2 5 0 4 17]'

The Discrete Impulse block has the following settings:

Delay (samples) = 2
Sample time = 1
Samples per frame = 1

The block's operation is shown in the figure below.

Dialog Box

The Main pane of the Minimum block dialog appears as follows.

Mode

Specify the block's mode of operation:

Value — Output the minimum value of each input
Index — Output the index of the minimum value
Value and index — Output both the value and the index
Running — Track the minimum value of the input sequence over time

For more information, see Description.

Index base

Specify whether the index of the minimum value is reported using one-based or zero-based numbering. This parameter is only visible when the Mode parameter is set to Index or Value and index.

Find the minimum value over

Specify whether to find the minimum value along rows, columns, entire input, or the dimension specified in the Dimension parameter. For more information, see Description.

Reset port

Specify the reset event detected at the RST input port when you select Running for the Mode parameter. The rate of the reset signal must be a positive integer multiple of the rate of the data signal input. This parameter is enabled only when you set the Mode parameter to Running. For information about the possible values of this parameter, see Resetting the Running Minimum.

Treat sample-based row input as a column

Select to treat sample-based length-M row vector inputs as M-by-1 column vectors. This parameter is only visible when the Find the minimum value of parameter is set to Each column.

Dimension

Specify the dimension (one-based value) of the input signal, over which the minimum is computed. The value of this parameter cannot exceed the number of dimensions in the input signal. This parameter is only visible when the Find the minimum value over parameter is set to Specified dimension.

Enable ROI processing

Select this check box to calculate the statistical value within a particular region of each image. This parameter is only available when the Find the minimum value over parameter is set to Entire input, and the block is not in running mode.

The ROI processing parameters appear as follows.

ROI type

Specify the type of ROI you want to use. Your choices are Rectangles, Lines, Label matrix, or Binary mask.

ROI portion to process

Specify whether you want to calculate the statistical value for the entire ROI or just the ROI perimeter. This parameter is only visible if, for the ROI type parameter, you specify Rectangles.

Output

Specify the block output. The block can output a vector of separate statistical values for each ROI or a scalar value that represents the statistical value for all the specified ROIs. This parameter is not available if, for the ROI type parameter, you select Binary mask.

Output flag

Output flag indicating if ROI is within image bounds

Output flag indicating if label numbers are valid

When you select either of these check boxes, the Flag port appears on the block. For a description of the Flag port output, see the tables in ROI Processing.

The Output flag indicating if ROI is within image bounds check box is only visible when you select Rectangles or Lines as the ROI type.

The Output flag indicating if label numbers are valid check box is only visible when you select Label matrix for the ROI type parameter.

The Data type attributes pane of the Minimum block dialog appears as follows.

Note The parameters on the Data type attributes pane are only used for complex fixed-point inputs. The sum of the squares of the real and imaginary parts of such an input are formed before a comparison is made, as described in Value Mode. The results of the squares of the real and imaginary parts are placed into the product output data type. The result of the sum of the squares is placed into the accumulator data type. These parameters are ignored for other types of inputs.

Rounding mode

Select the rounding mode for fixed-point operations.

Overflow mode

Select the overflow mode for fixed-point operations.

Product output data type

Specify the product output data type. See Fixed-Point Data Types and Multiplication Data Types for illustrations depicting the use of the product output data type in this block. You can set it to:

A rule that inherits a data type, for example, Inherit: Same as input
An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Product output data type parameter.

See Using the Data Type Assistant for more information.

Accumulator data type

Specify the accumulator data type. See Fixed-Point Data Types for illustrations depicting the use of the accumulator data type in this block. You can set this parameter to:

A rule that inherits a data type, for example, Inherit: Same as input
An expression that evaluates to a valid data type, for example, fixdt([],16,0)

Click the Show data type assistant button to display the Data Type Assistant, which helps you set the Accumulator data type parameter.