{"id":1725,"date":"2014-12-31T13:56:06","date_gmt":"2014-12-31T12:56:06","guid":{"rendered":"http:\/\/photo.zakkinen.net\/?p=1725"},"modified":"2021-03-11T14:59:52","modified_gmt":"2021-03-11T13:59:52","slug":"frequency-separation","status":"publish","type":"post","link":"http:\/\/photo.zakkinen.net\/en\/frequency-separation\/","title":{"rendered":"Frequency Separation","raw":"Frequency Separation"},"content":{"rendered":"

Recently I found an interesting article on frequency separation<\/a> on the Fstoppers’ pages <\/a>that made me curious about this method. Seems to be pretty much standard now for beauty retouching. I learned something, but the article left me with unsanswered questions:<\/p>\n

    \n
  1. Why is Linear Light the correct blend mode for rejoining the two layers created during frequency separation?<\/li>\n
  2. What exactly is the difference between addition and subtraction blend mode?<\/li>\n
  3. Why should there be a difference in the process depending on the colour-depth (8-bit versus 16-bit)?<\/li>\n<\/ol>\n

    So I decided to have a closer look. But first, I had to understand Blend Modes <\/a>in general. Might be worth starting there if you have never dealt with the subject before.<\/p>\n

    The Task<\/h1>\n

    We want to split one image into two such that one of the resulting images only contains fine detail, the other the large scale changes in colour and brightness. Take the following crop from a portrait as an example:<\/p>\n

    \"Skin-Demo-A\"<\/a><\/p>\n

    You can see pores, a light stubble, skin texture, and you can discern features like part of a nose, a line, shadows. Here the skin texture should end up in the first image, colours and larger shadows defining the shape in the second. Later on I’d like to combine the two images again in a way that we – unless we manipulated one of the images – get the original back.<\/p>\n

    “Why?”, you may ask. Simply because after this so called frequency separation you can retouch skin-tones without having to worry about the texture and vice versa. If I wanted to get rid of the red spot you can see top right, I’d just correct the colour and brightness and leave the texture alone. All the unmodified areas will, once blended again, look unchanged. The manipulated area will look very natural. So that’s why, I’ll show you how.<\/p>\n

    But before we start, some (very little) theory.<\/p>\n

    Frequencies<\/h1>\n

    Fine structures mean spatially rapid changes of brightness, or a strong local contrast. You can interpret the changes of brightness as a superposition of waves. Waves, you may remember from your physics lessons, have a frequency, in this case a spatial frequency. Fine structure means high frequency, changes over a larger distance means low frequency.<\/p>\n

    Frequency Filtering<\/h2>\n

    If you are an audiophile, you may have heard of high-pass or low-pass filters used in audio equipment. They do what their names say, the low-pass lets the low frequencies pass, i.e. the bass notes, while the high-pass does the same for high frequencies. For the latter, we indeed have a ready-made filter in Photoshop. It lets the high frequencies of an image pass and blocks the low frequencies yielding an image wich is mostly grey, close to 50 %, with little deviations on a small scale. You can control the scale – or as the audiophile might say, the cutoff frequency – with the radius parameter.<\/p>\n

    Photoshop also knows low-pass filters, only they are called differently. You may be able to identify them yourself. What evens out all the small scale changes? Blurring does. There are several blur filters available. For our purpose it does not really matter which one we choose, though you have to be careful with filters like surface blur or smart blur, as they tend to create sharp edges, which mean high frequency again. I personally would use the good old workhorse gaussian blur with a rather large radius.<\/p>\n

    Back to the Task – Splitting the Image<\/h1>\n

    First we have an Image A. We create two copies and modify one so we get a new image B that is different from the original A. In this example I used a gaussian blur with a radius of 6 pixels:<\/p>\n

    \"Skin-Demo-B\"<\/a><\/p>\n

    You see, all the fine structure is gone, no skin texture to speak of left.<\/p>\n

    Now I want to create another image C from the second copy that contains only the differences between original A and B. Should be easy, just take the second copy and use the Apply Image command of Photoshop with the blend mode Subtract with A as target and B as source and be happy. Unfortunately there is a catch.<\/p>\n

    Photoshop only allows values between 0 and 1 as result, everything below 0 and above 1 gets cut off. Not a very good idea when subtracting two very similar images, there will almost certainly be some pixels with values below 0. So what we actually do is:<\/p>\n

      \n
    1. divide by 2<\/li>\n
    2. add \u00bd<\/li>\n<\/ol>\n

      Thus the complete information is kept. The following formula is for a pixel-value of C:<\/p>\n

      \"c.<\/p>\n

      It is easy to see that nothingis lost when you look at the extremes, i.e. combinations of \"a,b.<\/p>\n

      Btw, I am showing all this for one channel only, for an RGB image this can be done for each channel separately.<\/p>\n

      The result of the “subtraction” is quite similar to that of Photoshop’s own High Pass filter – not exactly surprising.<\/p>\n

      \"Skin-Demo-C\"<\/a><\/p>\n

      Note<\/h2>\n

      Photoshop can handle images with a depth of 8-bit, 16-bit or even 32-bit per pixel. The 1 I talked about above correspondes to 255, 65536 or 4294967295 respectively. The apply image dialogue offers two paramerters for the blend mode subtraction, scale and offset. For our intention we need 2 for scale – that is for the aforementioned division by two, and 128 for offset. Bit hard to recognise the addition of \u00bd, but that is what it is. Regardless of the bit depth the offset has to be specified in parts of 256, and 128 divided by 256 happens to be \u00bd. This is confusing, and probably the reason for some more complicated workflows I have seen.<\/p>\n

      One mentioned frequently is this (for 16-bit images):<\/p>\n

        \n
      1. invert image B<\/li>\n
      2. add the result to A<\/li>\n
      3. set the scale-parameter to 2 (i. e. divide by 2)<\/li>\n<\/ol>\n

        Looking at the math I wasn’t able to find any difference to my method. My practical tests didn’t show any either, neither for 8-bit nor for 16-bit images. If you know that inversion just means subtracting the pixel value from 1, the formula is easy:<\/p>\n

        \"\frac{a+(1-b)}{2}.<\/p>\n

        So the answer to question three is: there is no difference.<\/p>\n

        Reassembly<\/h1>\n

        Now we just need another blend mode that can reassemble the two images B and C so that, if both are unchanged, we get A again. Simply adding the pixel-values won’t work of course, we scaled and shifted the result of the subtraction. So we need to find the reverse operation. So we subtract \u00bd from C, multiply the result by 2 and add B.<\/p>\n

        \"f(b,c).<\/p>\n

        Surprisingly this is exactly the formula for the Linear Light blend mode<\/a>. So my first question is answered as well: Linear Light is the reverse of Subtraction.<\/p>\n

        Using the Frequency Separation Technique<\/h1>\n

        In practice you will of course not use Apply Image to join the hard-won separate images immediately again. You will instead use both images as layers, C over B, and set the blend mode for C to Linear Light. So you keep two layers you can work on separately. Of course you can add layers between the two, for example for non-destructive retouching. In the example I was able to remove the red spot while keeping the texture. Retouching is not within the scope of this article.<\/p>\n

        \"Skin-Demo-Final\"<\/a><\/p>\n

        The remaining answer to question two you will find in my little series on Blend Modes<\/a> – with more math and simulations.<\/p>\n

        I hope you liked my little excursus on frequency separation. If you have questions or find mistakes, do not hesitate to leave a comment.<\/p>\n","protected":false,"raw":"Recently I found an interesting article on frequency separation<\/a> on the Fstoppers' pages <\/a>that made me curious about this method. Seems to be pretty much standard now for beauty retouching. I learned something, but the article left me with unsanswered questions:\n

          \n \t
        1. Why is Linear Light the correct blend mode for rejoining the two layers created during frequency separation?<\/li>\n \t
        2. What exactly is the difference between addition and subtraction blend mode?<\/li>\n \t
        3. Why should there be a difference in the process depending on the colour-depth (8-bit versus 16-bit)?<\/li>\n<\/ol>\nSo I decided to have a closer look. But first, I had to understand Blend Modes <\/a>in general. Might be worth starting there if you have never dealt with the subject before.\n

          The Task<\/h1>\nWe want to split one image into two such that one of the resulting images only contains fine detail, the other the large scale changes in colour and brightness. Take the following crop from a portrait as an example:\n\n\"Skin-Demo-A\"<\/a>\n\nYou can see pores, a light stubble, skin texture, and you can discern features like part of a nose, a line, shadows. Here the skin texture should end up in the first image, colours and larger shadows defining the shape in the second. Later on I'd like to combine the two images again in a way that we - unless we manipulated one of the images - get the original back.\n\n\"Why?\", you may ask. Simply because after this so called frequency separation you can retouch skin-tones without having to worry about the texture and vice versa. If I wanted to get rid of the red spot you can see top right, I'd just correct the colour and brightness and leave the texture alone. All the unmodified areas will, once blended again, look unchanged. The manipulated area will look very natural. So that's why, I'll show you how.\n\nBut before we start, some (very little) theory.\n

          Frequencies<\/h1>\nFine structures mean spatially rapid changes of brightness, or a strong local contrast. You can interpret the changes of brightness as a superposition of waves. Waves, you may remember from your physics lessons, have a frequency, in this case a spatial frequency. Fine structure means high frequency, changes over a larger distance means low frequency.\n

          Frequency Filtering<\/h2>\nIf you are an audiophile, you may have heard of high-pass or low-pass filters used in audio equipment. They do what their names say, the low-pass lets the low frequencies pass, i.e. the bass notes, while the high-pass does the same for high frequencies. For the latter, we indeed have a ready-made filter in Photoshop. It lets the high frequencies of an image pass and blocks the low frequencies yielding an image wich is mostly grey, close to 50 %, with little deviations on a small scale. You can control the scale - or as the audiophile might say, the cutoff frequency - with the radius parameter.\n\nPhotoshop also knows low-pass filters, only they are called differently. You may be able to identify them yourself. What evens out all the small scale changes? Blurring does. There are several blur filters available. For our purpose it does not really matter which one we choose, though you have to be careful with filters like surface blur or smart blur, as they tend to create sharp edges, which mean high frequency again. I personally would use the good old workhorse gaussian blur with a rather large radius.\n

          Back to the Task - Splitting the Image<\/h1>\nFirst we have an Image A. We create two copies and modify one so we get a new image B that is different from the original A. In this example I used a gaussian blur with a radius of 6 pixels:\n\n\"Skin-Demo-B\"<\/a>\n\nYou see, all the fine structure is gone, no skin texture to speak of left.\n\nNow I want to create another image C from the second copy that contains only the differences between original A and B. Should be easy, just take the second copy and use the Apply Image command of Photoshop with the blend mode Subtract with A as target and B as source and be happy. Unfortunately there is a catch.\n\nPhotoshop only allows values between 0 and 1 as result, everything below 0 and above 1 gets cut off. Not a very good idea when subtracting two very similar images, there will almost certainly be some pixels with values below 0. So what we actually do is:\n
            \n \t
          1. divide by 2<\/li>\n \t
          2. add \u00bd<\/li>\n<\/ol>\nThus the complete information is kept. The following formula is for a pixel-value of C:\n\n$latex c = f(a,b) = \\frac{a-b+1}{2}&s=1$.\n\nIt is easy to see that nothingis lost when you look at the extremes, i.e. combinations of $latex a,b \\in \\{0,1\\}$.\n\nBtw, I am showing all this for one channel only, for an RGB image this can be done for each channel separately.\n\nThe result of the \"subtraction\" is quite similar to that of Photoshop's own High Pass filter - not exactly surprising.\n\n\"Skin-Demo-C\"<\/a>\n

            Note<\/h2>\nPhotoshop can handle images with a depth of 8-bit, 16-bit or even 32-bit per pixel. The 1 I talked about above correspondes to 255, 65536 or 4294967295 respectively. The apply image dialogue offers two paramerters for the blend mode subtraction, scale and offset. For our intention we need 2 for scale - that is for the aforementioned division by two, and 128 for offset. Bit hard to recognise the addition of \u00bd, but that is what it is. Regardless of the bit depth the offset has to be specified in parts of 256, and 128 divided by 256 happens to be \u00bd. This is confusing, and probably the reason for some more complicated workflows I have seen.\n\nOne mentioned frequently is this (for 16-bit images):\n
              \n \t
            1. invert image B<\/li>\n \t
            2. add the result to A<\/li>\n \t
            3. set the scale-parameter to 2 (i. e. divide by 2)<\/li>\n<\/ol>\nLooking at the math I wasn't able to find any difference to my method. My practical tests didn't show any either, neither for 8-bit nor for 16-bit images. If you know that inversion just means subtracting the pixel value from 1, the formula is easy:\n\n$latex \\frac{a+(1-b)}{2} = \\frac{a-b+1}{2} = \\frac{a-b}{2}+{1\/2}&s=1$.\n\nSo the answer to question three is: there is no difference.\n

              Reassembly<\/h1>\nNow we just need another blend mode that can reassemble the two images B and C so that, if both are unchanged, we get A again. Simply adding the pixel-values won't work of course, we scaled and shifted the result of the subtraction. So we need to find the reverse operation. So we subtract \u00bd from C, multiply the result by 2 and add B.\n\n$latex f(b,c) = 2(c-1\/2) + b = 2c - 1 +b = b + 2c -1&s=1$.\n\nSurprisingly this is exactly the formula for the Linear Light blend mode<\/a>. So my first question is answered as well: Linear Light is the reverse of Subtraction.\n

              Using the Frequency Separation Technique<\/h1>\nIn practice you will of course not use Apply Image to join the hard-won separate images immediately again. You will instead use both images as layers, C over B, and set the blend mode for C to Linear Light. So you keep two layers you can work on separately. Of course you can add layers between the two, for example for non-destructive retouching. In the example I was able to remove the red spot while keeping the texture. Retouching is not within the scope of this article.\n\n\"Skin-Demo-Final\"<\/a>\n\nThe remaining answer to question two you will find in my little series on Blend Modes<\/a> - with more math and simulations.\n\nI hope you liked my little excursus on frequency separation. If you have questions or find mistakes, do not hesitate to leave a comment."},"excerpt":{"rendered":"","protected":false,"raw":""},"author":1,"featured_media":1733,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_de_post_content":"K\u00fcrzlich habe ich mich mit der Methode der Frequenztrennung zur Retusche besch\u00e4ftigt. Bei den Fstoppers habe ich einen einen interessanten Artikel<\/a> dazu gefunden, der mich aber mit Fragen zur\u00fcckgelassen hat. Eine war: warum ist Lineares Licht die richtige Verrechnungsmethode f\u00fcr die beiden Ebenen? Und direkt im Anschluss die Fragen, wo eigentlich der Unterschied zwischen Addition und Subtraktion bei der Bildberechung liegt und wieso man einen Unterschied zwischen 8bit und 16bit Bildern machen soll. Also wollte ich mir das mal genauer ansehen.\n\nDabei musste ich mir erst mal ein paar Gedanken zu Verrechnungsmodi (Blend Modes) <\/a>generell machen. Vielleicht lohnt es sich, mit dem Artikel <\/a>anzufangen.\n

              Aufgabenstellung<\/h1>\nEin Bild soll so in zwei zerlegt werden, dass das eine nur gro\u00dffl\u00e4chige Ver\u00e4nderungen beinhaltet, das andere die feinen Strukturen. Bei einem Portrait z. B. soll das erste Bild nur Farben und gro\u00dfe Strukturen wie Schatten beinhalten, die Hautstruktur soll sich im anderen wiederfinden. Die beiden Bilder sollen sich nachher \u00fcber Ebenenverrechnung wieder zu einem zusammensetzen lassen, das sich nicht vom Original unterscheidet.\n\n\"Skin-Demo-A\"<\/a>\n\nWarum? Weil man dann getrennt Korrekturen nur z. B. an der Hautfarbe machen kann, ohne die Struktur zu ver\u00e4ndern und umgekehrt. Nicht modifizierte Stellen ergeben das Original, an den Stellen, wo man retuschiert, sieht das Ergebnis sehr nat\u00fcrlich aus.\n

              Frequenzen<\/h1>\nFeine Strukturen bedeuten eine rasche \u00c4nderung der Helligkeitswerte, einen starken lokalen Kontrast. Man kann die \u00c4nderungen als \u00dcberlagerung von Wellen in der Fl\u00e4che sehen. Die feinen Strukturen bedeuten dann hohe Frequenzen, w\u00e4hrend die \u00c4nderungen \u00fcber gr\u00f6\u00dfere Abst\u00e4nde niedrige Frequenzen bedeuten.\n

              Frequenzfilter in Photoshop<\/h2>\nPhotoshop kennt einen Hochpassfilter, dessen Aufgabe es ist, feine Strukturen aus dem Bild zu holen. Es gibt auch Tiefpassfilter, die allerdings nicht so heissen. Was tut man, wenn man feine Strukturen, also die hohen Frequenzen, verschwinden lassen will? Man verwendet einen Weichzeichner (Blur). Welcher ist eigentlich egal, bei Filtern wie Matter Machen (Surface Blur) oder Selektiver Weichzeichner (Smart Blur) muss man allerdings etwas aufpassen, da hier scharfe Kanten entstehen, die eigentlich f\u00fcr hohe Frequenzen stehen.\n

              Bild zerlegen<\/h1>\nAm Anfang gibt es ein Bild A, davon erzeugt man zwei Kopien. Nun ver\u00e4ndert man die eine Kopie, so dass ein neues Bild B entsteht, z. B. mit einem Weichzeichner. Wie genau ist zun\u00e4chst egal. F\u00fcr das Beispiel habe ich einen Gaussschen Weichzeichner mit 6-Pixel-Radius verwendet.\n\n\"Skin-Demo-B\"<\/a>\n\nNun wird ein weiteres Bild C erzeugt, dass nur die Unterschiede zwischen A und B beinhaltet. Das sollte einfach sein, man muss nur die Differenz bilden. Praktisch macht man mit dem Men\u00fcbefehl Bildberechnung (Apply Image) mit A als Ziel und C als Quelle.\n\nNun ist aber zu beachten, dass Photoshop als Ergebnis einer Rechung nur Werte zwischen 0 und 1 zul\u00e4sst und alle anderen Werte abschneidet. Das ist bei der Differenzenbildung sehr ung\u00fcnstig, insbesondere, wenn die Bilder sehr \u00e4hnlich sind. Also dividiert man durch 2 und verschiebt um \u00bd nach oben, dann bleibt die komplette Information erhalten.\n\n$latex c = f(a,b) = \\frac{a-b+1}{2}&s=1$.\n\nDass dem so ist, sieht man leicht, wenn man sich die Extreme ansieht, also Kombinationen von $latex a,b \\in \\{0,1\\}$.\n\n\"Skin-Demo-C\"<\/a>\n

              Anmerkung<\/h2>\nIn Photoshop kann man mit 8-bit, 16-bit oder auch 32-bit pro Pixel und Farbe arbeiten. Die oben verwendete 1 entspricht dann 255, 65536 oder 4294967295. Der Dialog Bildberechnung (Apply Image) bietet f\u00fcr die Methode Differenz zwei Parameter an zum Skalieren und zum Verschieben. Zum Skalieren ben\u00f6tigt man die 2, das ist der oben genannte Divisor. Bei der Verschiebung kann man leider nicht 0,5 eintragen, sondern muss den entsprechenden 8-bit Wert verwenden, die 128, unabh\u00e4ngig von der Bit-Tiefe des Bildes. Das f\u00fchrt immer wieder zu Verwirrung, weshalb man auf manchen Webseiten den Hinweis findet, man solle im 16-Bit-Fall das Bild B unbedingt invertiert mit Skalierung 2 zu A addieren. Mathematisch ist das identisch, praktisch habe ich auch keinen Unterschied erkennen k\u00f6nnen, weder bei 8-bit noch bei 16-bit.\n\n$latex \\frac{a+(1-b)}{2} = \\frac{a-b+1}{2} = \\frac{a-b}{2}+{1\/2}&s=1$.\n

              Bild zusammensetzen<\/h1>\nJetzt gilt es noch, eine Formel zu finden, die die beiden Bilder B und C wieder zusammensetzt, so dass sich A ergibt. Einfach zusammenz\u00e4hlen geht nat\u00fcrlich nicht, weil skaliert und verschoben worden ist. Was ist zu tun? Ganz einfach: C verdoppeln, zu B hinzuz\u00e4hlen und 1 abziehen.\n\n$latex f(b,c) = b + 2c -1&s=1$.\n\nDas ist genau das, was die Verrechnungsmethode Lineares Licht<\/a> tut.\n

              Praktische Anwendung<\/h1>\nIn der Praxis wird man nicht einfach mit Bildberechnung (Apply Image) aus den m\u00fchsam getrennten Bildern gleich wieder eins machen. Man wird beide Bilder als Ebenen \u00fcbereinanderlegen, B nach unten, C nach oben, und f\u00fcr C den Verrechnungmodus Lineares Licht w\u00e4hlen. So beh\u00e4lt man zwei Ebenen, die man getrennt bearbeiten kann. Man kann auch weitere Ebenen dazwischenschieben, z.B. f\u00fcr die Korrektur von Hautt\u00f6nen oder einzelnen zu hellen oder dunklen Stellen. Ab hier wird es Retusche, und darum soll es in diesem Artikel nicht gehen.\n\n\"Skin-Demo-Final\"<\/a>","_de_post_name":"frequenzseparierung","_de_post_excerpt":"","_de_post_title":"Frequenztrennung","_en_post_content":"Recently I found an interesting article on frequency separation<\/a> on the Fstoppers' pages <\/a>that made me curious about this method. Seems to be pretty much standard now for beauty retouching. I learned something, but the article left me with unsanswered questions:\n
                \n \t
              1. Why is Linear Light the correct blend mode for rejoining the two layers created during frequency separation?<\/li>\n \t
              2. What exactly is the difference between addition and subtraction blend mode?<\/li>\n \t
              3. Why should there be a difference in the process depending on the colour-depth (8-bit versus 16-bit)?<\/li>\n<\/ol>\nSo I decided to have a closer look. But first, I had to understand Blend Modes <\/a>in general. Might be worth starting there if you have never dealt with the subject before.\n

                The Task<\/h1>\nWe want to split one image into two such that one of the resulting images only contains fine detail, the other the large scale changes in colour and brightness. Take the following crop from a portrait as an example:\n\n\"Skin-Demo-A\"<\/a>\n\nYou can see pores, a light stubble, skin texture, and you can discern features like part of a nose, a line, shadows. Here the skin texture should end up in the first image, colours and larger shadows defining the shape in the second. Later on I'd like to combine the two images again in a way that we - unless we manipulated one of the images - get the original back.\n\n\"Why?\", you may ask. Simply because after this so called frequency separation you can retouch skin-tones without having to worry about the texture and vice versa. If I wanted to get rid of the red spot you can see top right, I'd just correct the colour and brightness and leave the texture alone. All the unmodified areas will, once blended again, look unchanged. The manipulated area will look very natural. So that's why, I'll show you how.\n\nBut before we start, some (very little) theory.\n

                Frequencies<\/h1>\nFine structures mean spatially rapid changes of brightness, or a strong local contrast. You can interpret the changes of brightness as a superposition of waves. Waves, you may remember from your physics lessons, have a frequency, in this case a spatial frequency. Fine structure means high frequency, changes over a larger distance means low frequency.\n

                Frequency Filtering<\/h2>\nIf you are an audiophile, you may have heard of high-pass or low-pass filters used in audio equipment. They do what their names say, the low-pass lets the low frequencies pass, i.e. the bass notes, while the high-pass does the same for high frequencies. For the latter, we indeed have a ready-made filter in Photoshop. It lets the high frequencies of an image pass and blocks the low frequencies yielding an image wich is mostly grey, close to 50 %, with little deviations on a small scale. You can control the scale - or as the audiophile might say, the cutoff frequency - with the radius parameter.\n\nPhotoshop also knows low-pass filters, only they are called differently. You may be able to identify them yourself. What evens out all the small scale changes? Blurring does. There are several blur filters available. For our purpose it does not really matter which one we choose, though you have to be careful with filters like surface blur or smart blur, as they tend to create sharp edges, which mean high frequency again. I personally would use the good old workhorse gaussian blur with a rather large radius.\n

                Back to the Task - Splitting the Image<\/h1>\nFirst we have an Image A. We create two copies and modify one so we get a new image B that is different from the original A. In this example I used a gaussian blur with a radius of 6 pixels:\n\n\"Skin-Demo-B\"<\/a>\n\nYou see, all the fine structure is gone, no skin texture to speak of left.\n\nNow I want to create another image C from the second copy that contains only the differences between original A and B. Should be easy, just take the second copy and use the Apply Image command of Photoshop with the blend mode Subtract with A as target and B as source and be happy. Unfortunately there is a catch.\n\nPhotoshop only allows values between 0 and 1 as result, everything below 0 and above 1 gets cut off. Not a very good idea when subtracting two very similar images, there will almost certainly be some pixels with values below 0. So what we actually do is:\n
                  \n \t
                1. divide by 2<\/li>\n \t
                2. add \u00bd<\/li>\n<\/ol>\nThus the complete information is kept. The following formula is for a pixel-value of C:\n\n$latex c = f(a,b) = \\frac{a-b+1}{2}&s=1$.\n\nIt is easy to see that nothingis lost when you look at the extremes, i.e. combinations of $latex a,b \\in \\{0,1\\}$.\n\nBtw, I am showing all this for one channel only, for an RGB image this can be done for each channel separately.\n\nThe result of the \"subtraction\" is quite similar to that of Photoshop's own High Pass filter - not exactly surprising.\n\n\"Skin-Demo-C\"<\/a>\n

                  Note<\/h2>\nPhotoshop can handle images with a depth of 8-bit, 16-bit or even 32-bit per pixel. The 1 I talked about above correspondes to 255, 65536 or 4294967295 respectively. The apply image dialogue offers two paramerters for the blend mode subtraction, scale and offset. For our intention we need 2 for scale - that is for the aforementioned division by two, and 128 for offset. Bit hard to recognise the addition of \u00bd, but that is what it is. Regardless of the bit depth the offset has to be specified in parts of 256, and 128 divided by 256 happens to be \u00bd. This is confusing, and probably the reason for some more complicated workflows I have seen.\n\nOne mentioned frequently is this (for 16-bit images):\n
                    \n \t
                  1. invert image B<\/li>\n \t
                  2. add the result to A<\/li>\n \t
                  3. set the scale-parameter to 2 (i. e. divide by 2)<\/li>\n<\/ol>\nLooking at the math I wasn't able to find any difference to my method. My practical tests didn't show any either, neither for 8-bit nor for 16-bit images. If you know that inversion just means subtracting the pixel value from 1, the formula is easy:\n\n$latex \\frac{a+(1-b)}{2} = \\frac{a-b+1}{2} = \\frac{a-b}{2}+{1\/2}&s=1$.\n\nSo the answer to question three is: there is no difference.\n

                    Reassembly<\/h1>\nNow we just need another blend mode that can reassemble the two images B and C so that, if both are unchanged, we get A again. Simply adding the pixel-values won't work of course, we scaled and shifted the result of the subtraction. So we need to find the reverse operation. So we subtract \u00bd from C, multiply the result by 2 and add B.\n\n$latex f(b,c) = 2(c-1\/2) + b = 2c - 1 +b = b + 2c -1&s=1$.\n\nSurprisingly this is exactly the formula for the Linear Light blend mode<\/a>. So my first question is answered as well: Linear Light is the reverse of Subtraction.\n

                    Using the Frequency Separation Technique<\/h1>\nIn practice you will of course not use Apply Image to join the hard-won separate images immediately again. You will instead use both images as layers, C over B, and set the blend mode for C to Linear Light. So you keep two layers you can work on separately. Of course you can add layers between the two, for example for non-destructive retouching. In the example I was able to remove the red spot while keeping the texture. Retouching is not within the scope of this article.\n\n\"Skin-Demo-Final\"<\/a>\n\nThe remaining answer to question two you will find in my little series on Blend Modes<\/a> - with more math and simulations.\n\nI hope you liked my little excursus on frequency separation. If you have questions or find mistakes, do not hesitate to leave a comment.","_en_post_name":"frequency-separation","_en_post_excerpt":"","_en_post_title":"Frequency Separation","edit_language":"en","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[448],"tags":[452,453],"class_list":["post-1725","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-methoden","tag-frequenztrennung","tag-retusche"],"jetpack_featured_media_url":"http:\/\/photo.zakkinen.net\/wp-content\/uploads\/2014\/12\/Skin-Demo-Final.png","jetpack_shortlink":"https:\/\/wp.me\/p2DYS2-rP","jetpack_likes_enabled":false,"jetpack-related-posts":[{"id":1707,"url":"http:\/\/photo.zakkinen.net\/en\/ps-blend-modes-2\/","url_meta":{"origin":1725,"position":0},"title":"Photoshop Blend Modes - Part 2","author":"zakkinen","date":"19. January 2015","format":false,"excerpt":"I already introduced the blend modes Multiplication, Linear Dodge, Linear Burn and Linear Light in the first part of the series. In this article I'll add some more that might be interesting for photographers. For one particular blend mode there is a separate third part, beause it is rather complicated\u2026","rel":"","context":"In "Methods and Techniques"","block_context":{"text":"Methods and Techniques","link":"http:\/\/photo.zakkinen.net\/en\/category\/methods\/"},"img":{"alt_text":"Farbig Nachbelichten","src":"https:\/\/i0.wp.com\/photo.zakkinen.net\/wp-content\/uploads\/2015\/01\/EPS-ColorBurn.png?resize=350%2C200","width":350,"height":200},"classes":[]}],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/posts\/1725","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/comments?post=1725"}],"version-history":[{"count":23,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/posts\/1725\/revisions"}],"predecessor-version":[{"id":6115,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/posts\/1725\/revisions\/6115"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/media\/1733"}],"wp:attachment":[{"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/media?parent=1725"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/categories?post=1725"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/photo.zakkinen.net\/en\/wp-json\/wp\/v2\/tags?post=1725"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}