We exploit the Accumulator Array of the Hough Transform by finding collections of (2 or more) peaks through which a given sinusoid will pass. Such sinusoids identify points in the original image where lines intersect. Peak collection (or line aggregation) is performed by making a second pass through the edge map, but instead of laying points down in the accumulator array (as with the original Hough Transform), we compute the line integral over each sinusoid that corresponds to the current edge point. If a sinusoid passes through \ge 2 peaks, we deposit that sum/integral into a new accumulator array - an array that has a direct one-to-one correspondence with the original image. Thus, "Houghing the Hough" identifies points that correspond to corners, junctions or line intersections in image space. During initial peak collection, we include in the line integral only the most (locally) significant peaks while sifting out other (comparatively) weaker peaks from the current, as well as subsequent peak collections. This "contextual peak sifting" greatly reduces computation, the effect of noise and the occurrence of false positives. Virtual line intersections (vanishing points, occluded corners, etc.) are detected as peaks without proximate edge support. Results in real-world images show the technique performs well in identifying corners, junctions and intersecting lines in a variety of scenes containing man-made objects such as buildings, documents, etc.