More efficient PCA

README.md

@@ -1,6 +1,6 @@
 # Pulse JS
 
-Use a webcam to measure heart rate. See demo at <http://pulsejs.github.io>
+Use a webcam to measure heart rate. See demo at <http://altomani.github.io/PulseJS>
 
 ## TODO
 

index.html

@@ -69,7 +69,7 @@ <h1>Charts</h1>
                 <div id="chart2" style="width:640px; height:480px"></div>
 
                 <p>Spectrum</p>
-                <div id="chart3" style="width:640px; height:480px"></div>
+                <div id="chart3" style="width:1920px; height:480px"></div>
 
 
             </div>

js/pulse.js

@@ -45,7 +45,7 @@ function start() {
         if (frame < 30) {
             compatibility.requestAnimationFrame(tick);
             ++frame
-        } else if (frame < num_frames + 30 + 1) {
+        } else if (frame < num_frames + 30 + 3) {
             var f = frame - 30;
             compatibility.requestAnimationFrame(tick);
             if (video.readyState === video.HAVE_ENOUGH_DATA) {
@@ -65,7 +65,7 @@ function start() {
 
                 ++frame;
             }
-        } else if (frame === num_frames + 30 + 1) {
+        } else if (frame === num_frames + 30 + 3) {
             video.pause();
             video.src=null;
             findPulse(); 
@@ -78,25 +78,25 @@ function start() {
         // Gaussian blur
         var r = [], g = [], b = [];
         for (i = 0; i < num_frames; i += 2) {
-            r[i/4] = red[i] + 3*red[i+1]  + 3*red[i+2] + red[i+3];
-            g[i/4] = green[i] + 3*green[i+1]  + 3*green[i+2] + green[i+3];
-            b[i/4] = blue[i] + 3*blue[i+1]  + 3*blue[i+2] + blue[i+3];
+            r[i/2]=(red[i] + 3*red[i+1]  + 3*red[i+2] + red[i+3]);
+            g[i/2]=(green[i] + 3*green[i+1]  + 3*green[i+2] + green[i+3]);
+            b[i/2]=(blue[i] + 3*blue[i+1]  + 3*blue[i+2] + blue[i+3]);
         };
 
-        r = utils.normalize(r);
-        g = utils.normalize(g);
-        b = utils.normalize(b);
+        r = utils.normalize(utils.delinearize(r));
+        g = utils.normalize(utils.delinearize(g));
+        b = utils.normalize(utils.delinearize(b));
 
         var signals = utils.PCA([r, g]);
-        var spectrum = utils.spectrum(signals[1]);
+        var spectrum = signals.map(utils.spectrum);
 
         var pulse=0, max=0, i;
 
         for (i=0; i<num_frames;i++) {
             var frequency=(60.0/num_frames)*(i+0.5);
             if (frequency>0.5 && frequency<3) {
-                if (spectrum[i]>max) {
-                    max=spectrum[i];
+                if (spectrum[1][i]>max) {
+                    max=spectrum[1][i];
                     pulse=Math.round(frequency*60);
                 }
             }
@@ -110,7 +110,7 @@ function start() {
 
         $.plot("#chart2", signals.map(utils.addIndex) );
 
-        $.plot("#chart3", [ utils.addIndex(spectrum.slice(0,64)) ]);
+        $.plot("#chart3", spectrum.map(utils.addIndex) );
 
 
 

js/utils.js

@@ -1,7 +1,8 @@
 var utils = (function utils() {});
 
 utils.sum = function (arr) {
-	return arr.reduce( function(a, b) { return a + b; } );
+	var s = arr.reduce( function(a, b) { return a + b; } );
+	return s;
 }
 
 utils.mean = function (arr) {
@@ -34,8 +35,8 @@ utils.stdErr = function (arr) {
 }
 
 utils.normalize =function (arr) {
-	var s = utils.stdErr(arr)
-	return utils.center(arr).map( function (x) { return x / s } );
+	var s = utils.stdErr(arr);
+	return utils.center(arr).map( function (x) { return (x / s) } );
 }
 
 utils.covarAM = function (arr, mat) {
@@ -53,7 +54,7 @@ utils.covMatrix = function (mat) {
 utils.SVD = numeric.svd;
 
 utils.PCA = function (mat) {
-	return utils.dot(utils.SVD(numeric.transpose(mat)).V, mat);
+	return numeric.transpose(utils.SVD(numeric.transpose(mat)).U);
 }
 
 utils.spectrum = function (arr) {
@@ -68,4 +69,19 @@ utils.max = function (arr) {
 
 utils.addIndex = function (arr) {
 	return arr.map(function (x, i) { return [i,x]; });
+}
+
+utils.range = function (n) {
+	var i, a = [];
+	for (i = 0; i < n; i++) {
+		a.push(i);
+	}
+	return a;
+}
+
+utils.delinearize = function (arr) {
+	var l=arr.length, r=utils.range(l), 
+	 	beta = utils.covariance(arr, r)/utils.variance(r),
+	 	alpha = utils.mean(arr) - beta * utils.mean(r);
+	return arr.map(function(x, i) { return x-alpha-beta*i})
 }