measureSharpness

Measure spatial frequency response using Imatest eSFR chart

Syntax

sharpnessTable = measureSharpness(chart)

sharpnessTable = measureSharpness(chart,Name,Value)

[sharpnessTable,aggregateSharpnessTable] = measureSharpness(___)

Description

sharpnessTable = measureSharpness(chart) measures the spatial frequency response (SFR) at all slanted edge regions of interest (ROIs) of an Imatest^® eSFR chart [1]. The returned sharpness table includes the frequency for each ROI at which the response drops to 50% of the initial and peak values.

sharpnessTable = measureSharpness(chart,Name,Value) measures the SFR at all specified slanted edge ROIs, specifying additional parameters.

[sharpnessTable,aggregateSharpnessTable] = measureSharpness(___) also returns the average SFR of vertical and horizontal ROIs, using the input arguments of either of the previous syntaxes.

Examples

Measure Sharpness of Slanted Edges on eSFR Chart

Read an image of an eSFR chart into the workspace.

I = imread("eSFRTestImage.jpg");

Create an esfrChart object, then display the chart with ROI annotations. The 60 slanted edge ROIs are labeled with green numbers.

chart = esfrChart(I);
displayChart(chart,displayColorROIs=false, ...
    displayGrayROIs=false,displayRegistrationPoints=false)

Measure the edge sharpness in ROIs 25-28, and return the measurements in sharpnessTable. Include measurements of the MTF70 and MTF30 by specifying the PercentResponse name-value argument.

sharpnessTable = measureSharpness(chart,ROIIndex=25:28,PercentResponse=[70 30])

sharpnessTable=4×9 table
    ROI    slopeAngle    confidenceFlag        SFR           comment                          MTF70                                           MTF70P                                        MTF30                                       MTF30P                 
    ___    __________    ______________    ____________    ____________    ____________________________________________    ____________________________________________    ________________________________________    ________________________________________

    25       4.2268          true          {85x5 table}    {0x0 double}    0.061637    0.059828    0.053096    0.059827    0.061637    0.059828    0.053096    0.059827      0.107     0.1118    0.11037    0.11082      0.107     0.1118    0.11037    0.11082
    26       5.0814          true          {85x5 table}    {0x0 double}     0.18553     0.18604     0.18528     0.18562     0.18553     0.18604     0.18528     0.18562    0.26282    0.26497    0.26211    0.26385    0.26282    0.26497    0.26211    0.26385
    27       4.7787          true          {85x5 table}    {0x0 double}    0.069499     0.06935    0.063808     0.06899    0.069499     0.06935    0.063808     0.06899    0.21579    0.21794    0.21785    0.21775    0.21579    0.21794    0.21785    0.21775
    28       4.7966          true          {85x5 table}    {0x0 double}     0.19057     0.20361     0.19589     0.20006     0.19057     0.20341     0.19565     0.20006    0.26185    0.27258    0.26126    0.26972    0.26185    0.27241    0.26118    0.26972

Select the fourth row in the sharpness table, which corresponds to ROI 28. Display the SFR plot of the ROI.

idx = 4;
plotSFR(sharpnessTable(idx,:))

Print the MTF70 and MTF30 measurements of the ROI. Compare the measurements against the plot.

The MTF70 measurement of the red and blue color channels are slightly smaller than 0.2, while the MTF70 measurement of the green and luminance channels are slightly larger than 0.2. These measurements agree with a visual inspection of the SFR plot, on which an SFR value of 0.7 occurs at spatial frequencies around 0.2 line pairs per pixel.

mtf70 = sharpnessTable.MTF70(idx,:)

mtf70 = 1×4

    0.1906    0.2036    0.1959    0.2001

The MTF30 measurement of the blue color channel is noticeably smaller than the MTF30 measurement of the other color channels. This measurement agrees with a visual inspection of the SFR plot, on which the SFR curve of the blue channel drops off more quickly than the other channels.

mtf30 = sharpnessTable.MTF30(idx,:)

mtf30 = 1×4

    0.2619    0.2726    0.2613    0.2697

Input Arguments

chart — eSFR chart

esfrChart object

eSFR chart, specified as an esfrChart object.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'ROIIndex',2 measures the sharpness only of ROI 2.

ROIIndex — ROI indices

1:60 (default) | scalar | vector

ROI indices to include in measurements, specified as the comma-separated pair consisting of 'ROIIndex' and a scalar or vector of integers in the range [1, 60]. The indices match the ROI numbers displayed by displayChart.

Note

measureSharpness uses the intersection of ROIs specified by 'ROIIndex' and 'ROIOrientation'.

Example: 29:32

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

ROIOrientation — ROI orientation

'both' (default) | 'vertical' | 'horizontal'

ROI orientation, specified as the comma-separated pair consisting of 'ROIOrientation' and 'both', 'vertical', or 'horizontal'. The measureSharpness function performs measurements only on ROIs with the specified orientation.

Note

measureSharpness uses the intersection of ROIs specified by 'ROIIndex' and 'ROIOrientation'.

Example: 'vertical'

Data Types: char | string

PercentResponse — Value of frequency response

50 (default) | scalar | vector

Value of frequency response at which to report the corresponding spatial frequency, specified as the comma-separated pair consisting of 'PercentResponse' and a scalar or vector of integers in the range [1, 100].

Each value of PercentResponse adds two columns to the sharpnessTable and aggregateSharpnessTable output arguments. The columns indicate the frequency at which the SFR drops to the specified percent of the initial and peak values. For example, when PercentResponse has the value 50, both output tables have the columns MTF50 and MTF50P. These columns indicate the frequency at which the SFR drops to 50% of the initial value and peak value, respectively.

Example: 30

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char | string

Output Arguments

sharpnessTable — SFR measurements of edges

m-by-n table

SFR measurements of edges, returned as an m-by-n table. m is the number of sampled ROIs. n changes values depending on PercentResponse. The first five columns are always present and represent these variables:

Variable	Description
ROI	Index of the sampled ROI. The value of ROI is an integer in the range [1, 60].
slopeAngle	Angle between the slanted edge and pure vertical or horizontal, depending on the ROI orientation. The angle is measured in degrees, and it is returned as a scalar of type double.
confidenceFlag	Boolean flag that indicates whether the sharpness measurement is reliable. confidenceFlag is true when the measurement is reliable. confidenceFlag is false when the measurement is unreliable due to the following conditions: slopeAngle is less than 3.5 degrees or more than 15 degrees. The contrast within the ROI is less than 20%. The contrast of a slanted edge ROI is defined as 100 * (IHigh - ILow)/(IHigh + ILow), where IHigh and ILow are the estimated average intensities of the high and low intensity regions across the edge. The contrast is computed for only the red channel.
SFR	Spatial frequency response of the edge in the ROI. SFR is an f-by-5 table. The five columns represent the frequency value and the red, green, blue, and luminance values corresponding to that frequency. f is the number of frequency samples of the MTF. Luminance (Y) is a linear combination of the red (R), green (G), and blue (B) channels according to: Y = 0.213R + 0.715G + 0.072B
comment	When confidenceFlag is false, then comment describes the reason the measurement is unreliable. When confidenceFlag is true, then comment is the empty vector, [].

Each value of PercentResponse adds two columns that indicate the frequency at which the SFR drops to the specified percent of the initial and peak value. The format of each entry in the column is a 1-by-4 vector. The four elements correspond to the red, green, blue, and luminance channels, respectively.

aggregateSharpnessTable — Average SFR measurements of vertical and horizontal edges

table with one or two rows

Average SFR measurements of vertical and horizontal edges, returned as a table with one or two rows. aggregateSharpnessTable has one row when all sampled ROIs have the same orientation. It has two rows when the sampled ROIs have mixed orientation. aggregateSharpnessTable has three fewer columns than sharpnessTable.

The first two columns of aggregateSharpnessTable are always present and represent these variables:

Variable	Description
Orientation	Orientation of the averaged SFRs. The value of Orientation is either 'horizontal' or 'vertical'.
SFR	Averaged spatial frequency response of all edges in included ROIs with the orientation specified by Orientation. SFR is an s-by-5 table. The five columns represent the frequency value, and the averaged red, green, blue, and luminance values corresponding to that frequency. s is the number of frequency samples of the MTF. Luminance (Y) is computed as a linear combination of the red (R), green (G), and blue (B) channels according to: Y = 0.213R + 0.715G + 0.072B

Each value of PercentResponse adds two columns that indicate the frequency at which the SFR drops to the specified percent of the initial and peak value. The format of each entry in the column is a 1-by-4 vector. The four elements correspond to the red, green, blue, and luminance channels, averaged among all sampled ROIs with the same orientation.

Tips

• Slanted edges on a properly oriented chart are at an angle of 5 degrees from the horizontal or vertical. Sharpness measurements are not accurate when the edge orientation deviates significantly from 5 degrees.

• Sharpness is higher toward the center of the imaged region and decreases toward the periphery. Horizontal sharpness is usually higher than vertical sharpness.

Algorithms

The SFR measurement algorithm is based on work by Peter Burns [2] [3]. First, measureSharpness determines the edge position with sub-pixel resolution for each scan line, or row or column of pixels perpendicular to the edge, in the ROI. For example, each row of pixels is a scan line for a near-vertical edge. Next, measureSharpness aligns and averages the scan lines to create an oversampled edge intensity profile. The function takes the derivative of the intensity profile and applies a windowing function. The returned SFR measurement is the absolute value of the Fourier transform of the windowed derivative.

References

[1] Imatest. "Esfr". https://www.imatest.com/mathworks/esfr/.

[2] Burns, Peter. "Slanted-Edge MTF for Digital Camera and Scanner Analysis." Society for Imaging Science and Technology; Proceedings of the Image Processing, Image Quality, Image Capture Systems Conference. Portland, Oregon, March 2000, pp. 135–138.

[3] Burns, Peter. "sfrmat3: SFR evaluation for digital cameras and scanners." URL: http://losburns.com/imaging/software/SFRedge/sfrmat3_post/index.html.

Version History

Introduced in R2017b