Otsu method (graythresh function in matlab) gives scaled result, at what scale? 0: 255, 0: max (intensity px), min: max.
Just clarifying the question of Otsu's threshold method, which has no definition in the docs and wikipedia articles. If you use Otsu's method (a function in matlab graythresh
), it returns a threshold value between 0 and 1.
Given two hypothetical grayscale images:
-
dark
(with pixel intensities ranging from 0 to 100) and -
light
(with pixel intensities ranging from 155 to 255)
If I have an Otsu threshold of 0.75 for images dark
and thus light
what grayscale brightness will be displayed in each case?
-
dark -> 75
andlight -> 231
for example. relative to the range of values in each image -
dark -> 75
andlight -> 191
for example. relative to the range from 0 to maximum pixel value -
dark -> 191
andlight -> 191
for example. relative to the full range of grayscale pixel values (0-255)?
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The accepted answer by @Ratbert makes incorrect statements that
The correct answer is the first
and
graythresh
uses the min and max values in the image as boundaries, which is the most logical behavior.
and Rayryeng seems to agree with this. David Parks seems to have empirically confirmed this.
The correct answer is given by Anand, who, oddly enough, has a negative vote. He explains very convincingly that
full range of grayscale pixel values depends on the type input image
As he explains,
this is the third option
except that the image dark
cannot get a threshold of 0.75.
First, let's clarify the difference between the claims for the simplest case, in clear MATLAB, so there is no confusion. For an image with values from min
to max
, the question presents three possibilities, which when translated into an equation:
-
threshold = min + (max-min) * graythresh
-
threshold = max * graythresh
-
threshold = 255 * graythresh
Suppose the image consists of two points with an intensity of 0 and the other with 100. That means dark = uint8([0 100]);
. Second image light = dark+155;
. When we calculate 255*graythresh(dark)
, we get exactly 49.5
. When we calculate 255*graythresh(light)
, we get exactly 204.5
. These answers clearly indicate that the third option is the only option.
There is one more subtle point. If you try 255*graythresh(uint8(1:2))
, the answer is 1
, not 1.5
. So it seems that if you are using an greythresh
image for the threshold, you should use image <= 255*graythesh(image)
less than or equal, not equal less.
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Your third answer seems to me the most correct, with the clarification that the "full range of grayscale pixel values" depends on the data type of the input image. For example, for a uint8 image, the Otsu threshold of 0.75 corresponds to approximately 191. For a uint16 image, this would correspond to 49151.
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Ok, for posterity, I've made a comparison of the approaches mentioned above. I took a typical image with the full range of brightness in shades of gray, and then took the version dark
, and light
the same image, and received a value graythresh
for each. I have applied Otsu Threshold using each of the above mappings.
The light image demonstrates quite clearly that the algorithm creates a threshold in a range of pixel intensities. If we were to assume the full range of pixel intensities, Otsu's algorithm would create a threshold below whatever is present in the image, which doesn't make much sense, at least assuming the existing black background is transparent / inactive.
I'm guessing someone can make an argument to assume the full range of pixel intensities if you assume that the existing black portion of the image matches darkness. I would certainly welcome comments there.
Making changes to my words above: When I blacken everything except the top half of the image light
and get the Otsu threshold again, I get the same 0.3020 threshold. If the dark parts of the image related to Otsu's threshold were created, the extra darkness would affect the value, so Ratbert's answer is empirically demonstrated to be correct.
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