Changeset 1975

Timestamp:

11/16/07 02:34:32 (6 years ago)

Author:

sam

Message:

• Finished gamma correction section.

Location:

www/study

Files:

• fig4-1-3.png (added)
• fig4-1-3.svg (added)
• part4.html (modified) (4 diffs)

www/study/part4.html

@@ -96 +96 @@
 
 <p> The following figure shows the gamma curve for the naïve three-colour
-grayscale gradient we saw above (red) compared to the two-colour gradient
-(blue). Two major observations can be made: the new curve is far closer to
-a perfect, linear gradient, and there is a singularity in the middle of
-the curve, meaning a break in the gradient’s smoothness. </p>
+grayscale gradient we saw above (red curve) compared to the two-colour
+gradient (blue curve). Two major observations can be made: the new curve is
+far closer to a perfect, linear gradient, but there is a singularity in the
+middle of the curve, meaning a break in the gradient’s smoothness. </p>
 
 <p style="text-align: center;">
@@ -114 +114 @@
        is fixed. </li>
   <li> Don’t place the gray value at the middle of the gradient, for instance
-       putting it around 25% itensity will again match the previous two-colour
+       a value of around 25% intensity will again match the previous two-colour
        gradients. </li>
   <li> <b>Gamma-correct</b> input pixels before assigning them an output
-       value. This ensures that the resulting gradient is perfectly linear.
+       value. This ensures that the resulting gradient is perfectly linear
+       and has no singularity.
        </li>
 </ul>
@@ -123 +124 @@
 <h3> 4.2. Gamma correction </h3>
 
-<p> These are the results of gamma-correcting input pixels before doing
+<p> Gamma correction consists in converting pixel values into intensity values
+before performing operations on them, then reconverting them to pixel values
+before displaying them. The exact same algorithms can be used, they just
+operate on slightly different data. </p>
+
+<p style="text-align: center;">
+  <img src="fig4-1-3.png" width="460" height="256" alt="3-colour gamma coorection" />
+</p>
+
+<p> Here are the results of gamma-correcting input pixels before doing
 any computation on them, then using Floyd-Steinberg error diffusion: </p>
 
@@ -137 +147 @@
 </p>
 
-<!--
-<p> So, instead of using 25%, 50% and 75% patterns (which give non-uniform
-gray values of 0.53, 0.73 and 0.88), one should rather use 6.25%, 25% and 50%
-patterns, which give the better spread gray values of 0.28, 0.53 and 0.73
-and result in far more accurate gradients. This is especially obvious when
-observing the high intensity drop between the 25% pattern and black (top row):
-</p>
-
-<p style="text-align: center;">
-  <img src="pat005.png" width="400" height="240"
-       class="inline" alt="better gradients" />
-</p>
-
-<p> Here is the result on Lenna. As you can see, the result is visually less
-appealing than with the “incorrect” colours. But when seen from a distance,
-there is no doubt this version is more accurate: </p>
-
-<p style="text-align: center;">
-  <img src="out007.png" width="256" height="256"
-       class="inline" alt="gamma-aware 3-pattern halftoning" />
-  <img src="grad007.png" width="32" height="256"
-       class="inline" alt="gamma-aware 3-pattern halftoning gradient" />
-</p>
--->
-
-<!--
-<h3> Gamma with more gray levels </h3>
-
-<p> As seen previously, the smoothest dithering pattern that can be created
-with black and white is by uniformly alterning the two colours. However, the
-resulting colour (0.73) it is not evenly situated on the gray scale. </p>
-
-  <img src="out008.png" width="256" height="256"
-       class="inline" alt="gamma-aware 6.25%, 25% and 50% halftoning" />
-
-<p> Here is the application to Lenna, using the 0-0.2, 0.2-0.4, 0.4-0.6,
-0.6-0.8 and 0.8-1 ranges for black, white and the three patterns: </p>
-
-<p style="text-align: center;">
-  <img src="out005.png" width="256" height="256"
-       class="inline" alt="20/40/60/80% threshold and 25/50/75% halftones" />
-</p>
--->
+<p> Two-colour dithering is not visually satisfying: dark areas lack much
+detail because the gamma curve is very flat at low intensities. However,
+the result itself is far more accurate that previously. The problem, while
+still visible, is even less important with three-colour dithering: the image
+on the right is superior to what The Gimp or Adobe Photoshop are able to
+come up with. </p>
 
 <div style="float: left;">