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The power of standardized arithmetic

From: Photoshop Masking and Compositing: Advanced Blending

Video: The power of standardized arithmetic

Now as I mentioned at the outset of the course, this chapter is devoted to the underlying math associated with blending inside Photoshop. A few of you are going to find this information to be terribly useful, many of you are not. If you have any hesitations whatsoever, if you feel like the math is just going to overwhelm you or get in your way of understanding what's going on, then by all means skip ahead to the next chapter which is when we get down to the creative business of blending inside Photoshop. And do so knowing that skipping these movies will not adversely affect your understanding of this course one iota.

The power of standardized arithmetic

Now as I mentioned at the outset of the course, this chapter is devoted to the underlying math associated with blending inside Photoshop. A few of you are going to find this information to be terribly useful, many of you are not. If you have any hesitations whatsoever, if you feel like the math is just going to overwhelm you or get in your way of understanding what's going on, then by all means skip ahead to the next chapter which is when we get down to the creative business of blending inside Photoshop. And do so knowing that skipping these movies will not adversely affect your understanding of this course one iota.

However, if you have a mind for math and you feel like learning what's going on under the hood inside Photoshop might help you out, then stick with me. I'm working inside this file called Standardize arithmetic.psd and I've created a few layer comps in advance. I am going to go up to the Window menu and choose the Layer Comps command and then I am going to click the right pointing arrow head in order to switch to the next comp and hide that warning text. And notice that I have the Assyrian layer selected here inside the Layers panel. I am going to bring up the Blend Mode pop-up menu.

Now I want you to note that a few of the blend modes are named after their underlying arithmetic operators. For example, we've got Linear Dodge ( Add) which actually does add luminance levels to each other. So not surprisingly, we end up brightening the image considerably. And if the sum of any two pixels that is a pixel on the active layer and the pixel directly below it on the background layer, if that sum ends up being anything more than 255 for white, then it blows out, it gets clipped so we have a ton of clipping going on inside the image.

The opposite blend mode is Subtract and so if you choose Subtract what you end up doing is you're subtracting the luminance levels on the active layer from those on the background layer and not surprisingly, we end up getting a very dark image and many of the composite pixels are now clipped to black. When things end up turning out differently than you might expect, is when we Multiply and Divide. So if I choose the Multiply blend mode, which you would naturally expect, if we're actually multiplying luminance levels, which we are, then you might expect the image to become lighter, instead it not only grows darker, but it grows darker uniformly.

We have no clipping going on whatsoever. The Multiply mode never clips luminance levels unless they were already clipped in the first place. So in other words, there is no overly bright whites and there is no overly dark blacks. Next, if I switch to the opposite mathematical operator which would be Divide, we end up brightening the image like crazy and once again, we are clipping pixels all over the place. So what in the world gives? Well, I am going to go ahead and switch back to the Normal mode here and bring up that Layer Comps panel once again and advance to this next comp, Luminance levels and this brings us to our first slide which explains how you might naturally expect things to work inside Photoshop.

So, let's imagine that as usual a luminance level of 0 is black and a luminance level of 255 is white. That's how it is throughout Photoshop, and luminance levels for the most part do work on a channel by channel basis, by the way. So where're we working with values greater than 1 that is 1 all the way up to 255, then here is how things would go. Now you need to bear in mind that all blend modes rely on basic arithmetic operations that is Plus, Minus, Times, and Divide.

They may mix and match those operations ever once in a while, but every single blend mode uses basic arithmetic. When working with values greater than 1, division usually delivers the smallest results, meaning we would get the darkest composite image, then subtraction, addition and ending with multiplication is the top dog. So, if you were to multiply, you'd get a very bright image. For example, let's say we have two pixels, one with a luminance level of 204 which would be quite bright and the other with a level of 76 which would be very dark.

If we were to divide and let's say the 204 pixels on the background layer, because that's how it would work then 204 divided by 76 would give us 2.68 or very nearly black. That would be a very, very dark composite pixel. Subtract would give us 204 minus 76 which equals 128, which is, by the way, medium gray. If we were to add the pixels, we'd get 204+76 which would give us a level of 280 and since 255 is white that's beyond white so that pixel will be clipped to white.

Then where we'd to multiply those luminance levels, it would be 204 times 76 which would be 15,504, which is extremely clipped. Well, I am here to tell you that's not the way it works. To see exactly how things do work, I am going to switch to my last layer comp and notice that it's titled working with values between 0 and 1. Here is a deal. Blend modes use standardized value, and by that I mean, all the luminance levels where blend modes are concerned fit inside that 0 to 1 range.

So to figure out what the standardized value is, you just take the luminance level and divide it by 255. So black as always is 0, because 0 divided by anything is 0. White would be 255 divided by 255 which is 1 and medium gray would be 128 divided by 255 which is 0.5. Multiplication and subtraction decrease brightness while addition and division increase brightness. For example, in a standardized world, the pixel with a luminance level of 204 becomes 0.8.

The one with a level of 76 is now 0.3. So if we multiply those two pixels, we get 0 .8 times 0.3 which is a lower number 0.24. That translates to a luminance level of 61, which is a darker composite pixel. If we subtract these numbers we get 0.8 minus 0.3 which is 0.5 just as before medium gray. So subtract works the same way as it would where we're working with luminance levels. Add does as well, 0.8 plus 0.3 gives us 1.1 which translates to a luminance level of 280, the same thing we saw before, so it's clipped and then division gives us 0.8 divided by 0.3 which is a bigger number 2.67, because all these tiny numbers fit inside this larger number a lot more times.

That translates to a level of 261, which is exceedingly clipped. So as a result, Multiply darkens uniformly, by the way, no clipping at all. Subtract darkens and may result in clipping. Add brightens and may result in clipping as well and division brightens and almost always results in clipping. And that folks, is how the basic arithmetic operations work where blending is concerned here inside Photoshop.

Show transcript

This video is part of

Image for Photoshop Masking and Compositing: Advanced Blending
 
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  1. 1m 43s
    1. Welcome
      1m 43s
  2. 33m 15s
    1. When in doubt, blend
      2m 20s
    2. Where to find blending options
      4m 10s
    3. 27 blend modes, 6 groups
      4m 23s
    4. Opacity vs. Fill Opacity
      4m 41s
    5. The "Fill Opacity Eight"
      4m 59s
    6. Blending adjustment layers
      4m 43s
    7. Blend mode shortcuts
      7m 59s
  3. 27m 3s
    1. The power of standardized arithmetic
      6m 58s
    2. Photoshop's blending formulas
      5m 27s
    3. Darken formulas vs. lighten formulas
      4m 15s
    4. Contrast mode formulas
      7m 28s
    5. Inversion, cancelation, and HSL
      2m 55s
  4. 17m 50s
    1. Normal mode vs. Dissolve mode
      2m 11s
    2. Making a dynamic Dissolve effect
      2m 21s
    3. Creating a Dissolve text effect
      4m 48s
    4. The Behind and Clear modes
      3m 2s
    5. Filling a stroke with Behind and Clear
      5m 28s
  5. 43m 24s
    1. Darken vs. Darken Color
      4m 25s
    2. Creating filter effects with Darken
      5m 0s
    3. The Multiply and Burn modes
      6m 27s
    4. Cleaning up scanned line art
      7m 30s
    5. Comping line art against a photo
      5m 12s
    6. Colorizing comped line art
      5m 14s
    7. Masking with a darken mode
      3m 59s
    8. Refining a mask with Multiply
      5m 37s
  6. 33m 36s
    1. Lighten vs. Lighter Color
      2m 29s
    2. Creating filter effects with Lighten
      2m 47s
    3. The Screen and Dodge modes
      4m 35s
    4. Blending white type, darkening shadows
      3m 2s
    5. Creating a classic double-exposure effect
      3m 49s
    6. Making dark line art bright
      5m 11s
    7. Masking with a lighten mode
      5m 4s
    8. Refine, filter, and blend
      6m 39s
  7. 35m 18s
    1. Overlay, Soft Light, and Hard Light
      5m 2s
    2. Vivid, Linear, and Pin Light
      4m 2s
    3. The amazing Hard Mix mode
      3m 51s
    4. Two variations on a single mode
      5m 37s
    5. Adding clarity with a contrast mode
      4m 9s
    6. Creating a glowing, soft-focus effect
      3m 38s
    7. Blending an image with a paper texture
      4m 11s
    8. Turning flesh into stone
      4m 48s
  8. 18m 10s
    1. Difference, Exclusion, Subtract, and Divide
      7m 7s
    2. Comparing seemingly identical images
      3m 25s
    3. Creating type that inverts any background
      3m 30s
    4. Making inversion type black and white
      4m 8s
  9. 16m 57s
    1. Luminosity, Color, Hue, and Saturation
      3m 29s
    2. Colorizing artwork with layers
      7m 24s
    3. Correcting skin tones with Hue
      6m 4s
  10. 14m 57s
    1. Using the This Layer slider option
      6m 44s
    2. Using the Underlying Layer slider option
      3m 16s
    3. Achieving greater control with Blend If
      4m 57s
  11. 48s
    1. Next steps
      48s

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