June 10, 2004


Histograms, Filtering and Signal-to-Noise

This exercise uses either the Leafnorm.tiff image or a porition of it, as decribed in the Histograms - Introduction exercise. See that exercise for the effects of intensity scaling (contrast and brightness adjustment) on an image.

The LUT and Map windows should look like this (except this is sideways to save space):

This is the 'normal' histogram for this image, against which the modifications below should be compared.

This is the smaller peak to the left. (That the darker objects correspond to the left peak can be verifed using the threshold tool - see the Histograms - Introduction exercise.) The peak is more jagged (noisier) because of the smaller number of pixels being sampled.


The Count is simply a tally of the number of measurements that have been done since clearing or saving them. This is of no particular use here.

Pixels = 50x70.

ImageJ - see below.

(Oops. The units of measurement have been set to inches. Resetting to pixels:)

Area: now same as the previous pixel count.
Mean: Mean intensity of pixels within the selection.
Std Dev: Standard deviation of pixels in the selection.
Min, Max: Lowest and highest pixel intensity in the selection.

ImageJ:  this is what the results window looks like for a similar selection. 

Note that the standard deviation in this selection is roughly the half width at half maximum of the histogram peak:

This corresponds to the right side of the peak of the histogram for the whole image.

ImageJ has this measurements table:

Note about visibility:

The visibility of objects depends on the signal to noise ratio. As the noise level increases, objects of the same contrast become more difficult to see. Most simple objects are barely visible with a K of 8 - 10 *, where K is the object signal to noise ratio.

In this case,

K = Signal / Noise

K = (Av level leaf - Av level Background) / (Std dev / sqrt (3500))

K = (135 - 92) / (11 / 59) = 43 * 59 / 11

K = 230

The 'leaves' in this image are quite visible - they have a high signal-to-noise ratio. This can be demonstrated by using a form of contrast enhancment called histogram equalization.

(Map window not in ImageJ.)

The contrast has been enhanced in such a way that equal gray level intervals correspond to equal areas in the image. In other words, the histogram should be flat. The LUT brightness function in the Map window generally has to be curved to to this. This is about the strongest kind of automatic contrast enhancement available, other than what results from the Options -> Threshold (Image / Adjust / Threshold). menu , and often is too contrasty. If the image had low signal to noise, the leaves would not be more visibile as they appear to be here - they would be obscured by equally contrasty noise.

* Bright, D.S. , D.E. Newbury and E. B. Steel, "Visibility of objects in computer simulations of noisy micrographs", J. of Microscopy 189(8):25-42, March 1997. (also see references to Albert Rose in this paper).

While here, examine the histogram of the equalized image to see if the histogram is really flat.

The histogram looks anything but flat, but remember the restriction that gray levels cannot be split - they are integers. If you could chop off the tall lines to fill in the gaps between them, the histogram would be fairly flat.


Smoothing using either the mean or median filter reduces the signal-to-noise by 'signal averaging'. The signal (difference in brightness between the leaves and the background) is not much affected because the leaves are much larger than the smoothing kernel, which is 3x3.

Note the smoothed appearance of the selection (most operations and measurements work only on a selection, if there is a selected region or line),

the reduced standard deviation:

and the narrowed peak in the histogram:



Smoothing the entire image smooths the histogram, narrows the peaks, and separates the peaks:

(just for comparison).

(mean filter smoothing)

Although the peaks in the histogram are more separated for the filtered images, this does not mean that filtering is desirable before segmenting (thresholding) the image to measure the leaves.

Additional Exercises