Image Statistics

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Image Statistics is an interactive utility introduced in Imatest 5.0 that lets you examine a number of image properties, including

• Vertical and horizontal cross-sections with adjustable thickness. Using a larger thickness mitigates the effects of noise.
• Properties of rectangular or square (eyedropper) regions, including rectangle position, Mean values of R,G,B, and Y (luminance) channels, Log10(mean/max), Noise (sigma), Noise corrected for nonuniformity, SNR (Signal/Noise), SNR dB, and Mean L*a*b* (when color space has been entered).
• Histograms (primarily Luminance channel: R, G, and B channels can be included) for rectangular regions with area greater than 250 pixels.
• Fourier spectrum with linear or logarithmic axes for rectangular regions larger than 100×100 pixels.
• 3D Surface plot, containing spatial pixel level information (Imatest 5.2+)
• All points below and/or above specified values as blue and/or red, respectively.
• Distance between points in the original image.
• EXIF data— metadata stored in the image file
 News: Imatest 5.2 has a pixel-level 3D surface plot with spatial information.

Image Statistics works with any image— not just test charts. It has a number of useful applications, for example,

• For Color/Tone Setup, Color/Tone Auto, and Stepchart you can determine the black level (pixel) offset (a fixed number added to the pixel level) and saturation level for an image.
• Noise may be added to the image after a black level offset has been applied. For this reason the minimum pixel level may not correspond to the offset. The peak of the histogram is a better indicator.
• The saturation level  is usually the maximum for the bit depth: 255 for 8-bits (24-bit color) and 65535 for 16-bits (48-bit color), but not always. We have seen 8-bit images that saturate (no longer increase in pixel level as patch brightness increases) around levels 220-235.

You may zoom or lighten the image to view details you might otherwise miss. Zooming makes it easier to select small or tight rectangular regions. It also limits the extent of cross-section displays (so that only regions of interest are displayed). Lightening the image does not affect the numeric results. Images with bit depths of 8 and 16 are supported.

Running Image Statistics

Image Statistics can be opened from

• the Image Stats button in the Utilities tab on the right of the Imatest main window or the Utilities dropdown menu,
• Rescharts, Color/Tone Setup, or Uniformity Interactive, either from the File dropdown menu or from a button in the control area on the right that appears when it’s not used for other purposes,
• Image Processing, from the Analysis dropdown menu. If both input and output images are present, the two images can be rapidly switched for comparison.

Opening Image Statistics brings up the following window. Brief instructions are shown below the image.

Image Statistics opening window

The window shows the uncropped image in its original brightness (unless it was changed in a previous run). The file name is at the top and a control area is on the left. There are several things you can do prior to performing one of the image analyses.

 You can downsample the image, which speeds up operations (especially cross-sections), with the Resize large images dropdown menu (upper-left). Settings 1. Do not resize or 2. Resize large images (imresize) are recommended. Downsampling is not recommend if noise or frequency spectrum are to be analyzed. Settings 3+ (resizing by skipping pixels) are not generally recommended. They have been used to diagnose some unusual demosaicing behavior. You can zoom the image by clicking and dragging the mouse. You can restore it by pressing Full view (zoom out) or by double-clicking on the image (which doesn’t always work). This can make it easier to select small rectangular regions or limit the extent of cross-sections so, for example, you can examine behavior in deep shadows. You can alter the appearance of the image— lighten it, increase saturation, tone map it, etc.— by clicking on the dropdown menu on the upper-left (that shows Original image above). Selections are shown on the right. Lightening the image (there are several methods) enables you to see shadow detail that is invisible in dark images. Altering the image appearance does not affect any of the numeric or graphic analysis results. You can click one of the settings in the Show pixels < or > set level panel to display all pixels lower than a set value as blue and/or higher as red. Set the boxes to 0 for normal display. Image appearance selections. They do not affect numeric results Background shown in yellow when anything but Original image is selected.

Here is an image shown zoomed in and lightened where pixels with a level is under 4 (of 255) are shown in blue and over 252 are shown in red. The zoom remains unchanged while Cross section, Rectangle/Eyedropper and other operations are performed. Click Full view (zoom out) to view the entire image.

Image Statistics zoomed in, lightened, pixels under 4 (of 255) shown in blue

Cross sections

Pressing X-Cross section or Y-Cross section in the Cross section panel turns on cross-hairs for selecting a horizontal or vertical cross section. You simply need to click on a point in the image to select the desired cross section, which will be contained inside a pair of red lines (vertical, left of center, in the image below). Dragging the mouse has no effect in Cross section mode. Click on a point outside the image (but not on an active button or text) to turn off the cross-hairs and return to normal mode. Note that most buttons are disabled or made invisible when Cross section mode is active. You need to make settings prior to pressing X or Y-Cross section. (Or course you can always change settings.)

Image Statistics, shown with Y (Vertical) Cross Section active, zoomed in.
This file had bit depth = 8. Files with bit depth = 16 tend to show more shadow detail.

Examining the vertical cross-section (with a logarithmic y-axis) enabled us to understand the behavior of this chart/camera combination in very dark areas, where it’s difficult to accomplish visually (we observed short-distance flare light that affected the results). The relatively wide line helped reduce the high noise in the deep shadow region.

Cross section settings  Several options are available for Cross section selection and plots.

• The Line width dropdown menu lets you select the width of the Cross section. Settings are 1, 3, 5, 7, 9, 11, 13, 15, 21, or 25 pixels. Increasing the value from the default of 1 reduces the noise (by 3 dB every time the width is doubled). In typical cases line width should be set as large as possible within the bounds of the features of interest. The cross section width is contained within the two vertical or horizontal red lines.
• The plot type dropdown menu lets you select (1) Plot R G B Y (equal emphasis), (2) Plot R G B Y (Y-emphasis) (default; recommended), or (3) Plot Y (luminance)-only.
• The y (vertical axis) dropdown menu lets you select (1) Linear y-axis, (2) Log10 y-axis (unnormalized), or  (3) Log10 y-axis (normalized). The choice depends on the application: the above chart had logarithmic steps (defined by density units), so a Log10 axes was selected.

Rectangle/Eyedropper analysis

This analysis allows you to examine several properties of rectangular regions (selected by clicking and dragging the mouse) or square eyedropper regions (selected by a simple mouse click—no drag). You can examine basic statistics, which includes means, noise (without and with a nonuniformity correction), CIELAB L*a*b* values, etc. Or you can view a histogram or frequency spectrum of the region. Click outside the image to turn off the Rectangle/Eyedropper selection. The rectangle and results will remain visible until the next selection is made. Here are the settings.

 Selection Measurement Standard Statistics Rectangle position, size, and diagonal length RGBY Mean, Noise (corrected and uncorrected), SNR, CIELAB L*a*b* values. Note: RMS noise is the same as standard deviation (σ). Histogram (Y)  full x-axis Histogram (Y)  expand x-axis Histogram (Y)+RGB  full x-axis Histogram (Y)+RGB  expand x-axis Display a histogram of log10(occurrences+1) for the luminance (Y) channel as a bar plot. Minimum region size = 250 pixels. Means are displayed as diamonds ◊ (for the Y-channel) and asterisks * (R, G, and B). Full x-axes is minimum to maximum for the image (0 to 1, 255, or 65535, depending on the image source and bit depth). Expand x-axis uses the upper and lower limits of the data to determine the x-axis. +RGB adds a stairs plot for the RGB channels to the histogram. Example below. Fourier spectrum Linear (>80×80) Fourier spectrum Log  (>80×80) One-dimensional plot the 2D Fourier frequency spectrum of the region with linear or logarithmic x and y-axes. Minimum region size = 80×80 pixels. Example below. 3D Surface plot 3D plot showing pixel level as a function of x,y location. Can be rotated. Must be turned off then back on to select a new region.

Additional settings include

• Eyedropper size. Settings are 1, 3, 5, 7, 9, 11, 13, 15, 21, or 25 (lengths of the sides in pixels).
• Color space (dropdown menu) which is used for calculating CIELAB L*a*b* values. Most common color spaces are available: sRGB (the Windows/internet standard) is the default.

Examples:

Rectangle/Eyedropper standard statistics: Crop of window showing rectangle

Histogram (Y)+RGB  expand x-axis:  Y (luminance) channel is a bar plot; RGB channels are stairs plots.
The change in noise when increasing Exposure index is highly visible in this plot.

Frequency spectrum with logarithmic axes of a Spilled Coins (Dead Leaves) chart
taken with a high-quality camera phone at 900 lux (bright light; low noise).

A logarithmic first order fit the exponent of the data curve (for the lower third of the data points) is shown as a dotted thin black line. For this pattern the fit is proportional to frequency−0.989. The original chart was designed to have a scale-invariant 1/f (frequency−1) frequency spectrum— very close to the fit. The image was not downsampled, i.e., Resize large images, which would affect results, was unchecked.

This plot lets you quickly observe the frequency spectrum of any image.

• You can look at high quality images of various Dead Leaves and (Imatest) spilled coins charts. We have found that the Imatest Spilled Coins chart is very close to a -1 exponent, which ensures true scale invariance. Other commercially-available Dead Leaves charts have exponents closer to 0.9.
• An “average scene” (a mythological beast if ever there was*) is supposed to have an exponent around -1. This is part of the justification for the design of the Dead Leaves and Spilled Coins charts (along with scale-invariance). You can look at the spectrum for any scene (or portion of a scene) to try to verify this.

*It’s very challenging to find an “average” scene here in Boulder, Colorado, where all scenes (not to mention people) are above average.
(Apologies to Garrison Keillor.) The spectral response of “above average” scenes has never been studied. Might make a good PhD thesis topic.

3D Surface plot (spatial analysis)

The 3D surface plot (Imatest 5.2+) displays spatial pixel information for the selected region. To view this plot, select Surface plot 3D  (standard or extra smoothing) in the dropdown menu just below the Rectangle analysis button, press Rectangle analysis, then select a region to display The plot can be rotated by dragging with a mouse. Because the selected region is usually covered by the surface plot, a replica of the selection is displayed to the left. To analyze a different region, click the  Restore control buttons & original image  button on the left, then press Rectangle analysis again. (This is slightly different from other rectangle analyses, where you can simply select a new region.)

3D Surface plot, showing pixel levels as a function of location
for an 8-bit (256-level) image with low random noise but clear quantization noise

This plot displays spatial information. In this case we can clearly see how the limited number of digital levels (0-255) affects the noise measurement.

Other controls

Full view (zoom out) restores the original full image view: it zooms out the image (double-click often doesn’t work).

Data cursor lets you see a Data cursor when you click on the image. Example on right. Click on Data cursor (toggle button, which has a yellow background when active) to turn this function on or off. Right-click on the data cursor to remove it.

EXIF displays selected EXIF data (metadata contained in the file) below the image. For full EXIF data, use the File dropdown menu (Phil Harvey’s EXIFtool must be installed and selected).