Update proj1.html

Author: cjxthecoder

project-1/proj1.html

@@ -187,7 +187,7 @@ <h2>Image Pyramid</h2>
 
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-Even for small images, the pyramid method achieved a speedup of over 100x, while for large images, the computation time is still faster than what naive search takes on a single small image. More concretely, because the image is downscaled by 2x at each layer of the pyramid, the total image area is less than 1 + (1/2)<sup>2</sup> + (1/4)<sup>2</sup> + (1/8)<sup>2</sup> + ... = 1 + 1/4 + 1/16 + 1/64 + ... &lt; 4/3 of the original. Since the search at the lowest scale is limited to W &leq; 72, the total time complexity is only <i>4(3W)W / 3</i> + smaller terms = <i>O(W<sup>2</sup>)</i>, at least a full width factor faster than the naive method.
+Even for small images, the pyramid method achieved a speedup of over 100x due to a reduction in both size and number of NCC computations, while for large images, the computation time is still faster than what naive search takes on a single small image. More concretely, because the image is downscaled by 2x at each layer of the pyramid, the total image area is less than 1 + (1/2)<sup>2</sup> + (1/4)<sup>2</sup> + (1/8)<sup>2</sup> + ... = 1 + 1/4 + 1/16 + 1/64 + ... &lt; 4/3 of the original. Since the search at the lowest scale is limited to W &leq; 72, the total time complexity is only <i>4(3W)W / 3</i> + smaller terms = <i>O(W<sup>2</sup>)</i>, which matches with the actual factor of ~100 between the time it takes to align .jpg and .tif files.
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