Clean up chroma display and improve alpha metric

web/metrics.js

@@ -19,7 +19,7 @@ const metrics = {
     option: "Geometric Difference (α)",
     displayName: String.raw`\alpha`,
     displayBody: p => String.raw`
-      \sqrt{\sigma\left(${p}\right)\Theta\left(${p}\right)}
+      \sqrt{\sigma\left(${p}\right)^{2 - L\left(\vec{q}\right)} \Theta\left(${p}\right)^{L\left(\vec{q}\right)}}
     `,
     evaluate: () => 0, // calculated below
   },
@@ -93,9 +93,7 @@ const metrics = {
   chroma: {
     option: "Mean Chroma (C)",
     displayName: "C",
-    displayBody: (p, space) => String.raw`
-      \text{chroma}\left(\vec{\mu}\left(${p}\right)\right)
-    `,
+    displayBody: p => String.raw`\text{chroma}\left(\vec{\mu}\left(${p}\right)\right)`,
     evaluate: data => data.mu.chroma,
   },
   muNuAngle: {
@@ -118,6 +116,6 @@ const applyMetrics = (data, target) => {
       .map(([name, metric]) => [name, metric.evaluate(data, target)])
   );
   // rearranges to geometric mean of sigma and bigTheta
-  scores.alpha = Math.sqrt(scores.sigma * scores.bigTheta);
+  scores.alpha = Math.sqrt(Math.pow(scores.sigma, 2 - target.lightness) * Math.pow(scores.bigTheta, target.lightness));
   return scores;
 };