Histograms – Chapter 4

Huh?

• That image is too contrasty.

• The colors aren’t vibrant enough.

• I want the reds to pop.

• It doesn’t have a warm enough feel.

• etc. etc. etc.

• The industry is rife with such statements that no one really knows how to interpret consistently

Some examples

Some examples

The goal

• We know when a picture “looks” good• We know when a picture “looks” bad

– But this is purely subjective

• Sometimes we know what the reality is– But sometimes one person’s reality is different

than another’s

• Sometimes we have no idea what reality is– The scene we photographed is long gone

• We need a way to quantify our findings

Statistics…

• Figures often beguile me, particularly when I have the arranging of them myself; in which case the remark attributed to Disraeli would often apply with justice and force: "There are three kinds of lies: lies, damned lies and statistics." – Mark Twain

Statistics

• Statistics can tell us a lot about an image– Quality of exposure– Image manipulations– Compression/quantization

Statistics

• But if we compute the statistics in the “usual way” all we get is a bunch more numbers to look at– Min– Max– Mean– Mode– Skew– Standard deviation– etc.

• A picture is worth a thousand words (or number in this case)

Histogram

• Pictorial depiction of image statistics

Histogram

• The pixels within an image are arranged in a spatially coherent manner– What does that mean?

• Their position in the image matters

• A histogram is a frequency distribution of the pixel values within an image– What does that mean?

• It depicts the number of times a particular pixel value occurs in the image

Histogram

• Mathematically speaking…

• In words: h(i) is the number of pixels in the image I who’s value is i

• It will contain an array of values, 1 for each possible pixel value K

}),(|),{()( ivuIvucardih

Ki 0

Histogram

• The histogram does not contain any spatial information whatsoever!– Can you reconstruct the original image

from the histogram?• No, just like if I give you a bunch of statistics

you can’t recreate the original dataset!

What can you do with a histogram?• Image Acquisition – exposure

• Where the concentration of pixel values lie within the histogram

• Laymen’s (subjective) terms: how bright or dark is the image

Under exposed

Over exposed

Properly exposed

What can you do with a histogram?• Image acquisition – contrast

• How much of the pixel value range is effectively used – Note that “effectively” is yet another

subjective term

• Laymen’s (subjective) term: how foggy is the image

Low contrast

High contrast

“Good” (normal?) contrast

What can you do with a histogram?• Image acquisition – dynamic range• The number of distinct pixel values in the

image• Often times this dynamic range will consider

how much “noise” (unstructured, unwanted, unintended, modifications of the pixel values) as part of the definition

• Laymen’s (subjective) term: how posterized or contoured is the image

Very, very low dynamic range

Low dynamic range

High dynamic range

A test image

Test image

• Exposure?

• Contrast?

• Dynamic range?

ImageJ

• Open snake.png (download from my web site)• Select Analyze/Histogram

– This is the histogram of the luminance channel of the color image

• Select Image/Color/Split Channels– You now have the red/green/blue channels individually

• Create histograms of each of these• Comment on exposure, contrast, dynamic range• Pull other images from wherever, play with it