FDS-PROJECT

1. Image Filtering (10 points)
   1.d What happens when you apply the following Filter combinations?

   1. First Gx, then Gx^T
      First we smooth the image in the horizontal direction by applying the single-dimensional Gaussian matrices Gx, then then we repeat the process in the vertical direction Gy = Gx^T. It has the same effect of applying a two-dimensional gaussian matrix because the gaussian filter is a separable one. In computational terms, applying the independent one-dimensional filter is more efficient, since the calculation can be performed in O(n) rather than O(n^2). Each pixels of the blurred image are set to a weighted average of that pixel’s neighborhood. The original pixel's value receives the heaviest weight (having the highe Gaussian value) and neighboring pixels receive smaller weights as their distance to the original pixel increases.

   2. First Gx, then Dx^T
      First we filter the image in the horizontal direction by applying Gx and this will give us pixels with higher intensity at the img_imp [13, 13] where we have the impulse and gets less brighter as the neighboring pixels receive smaller weights as their distance to the original pixel increases. When then we apply the derivative filter in the vertical direction what happens is that it detects edges in the horizontal direction by increasing and decreasing the intensity of pixels below and above the edge, respectively.

   3. First Dx^T , then Gx
      This filter combination has the same effect of question number two because of the linear operation of convolution and derivative, therefor applying first the derivative filter and then the smoothing operation or vice versa is not going to change the final output image.

   4. First Dx, then Dx^T
      By applying a first order differentiation in horizontal and vertical direction we detect vertical edges and horizontal edges respectively, so Dx sets pixels with higher intensity to the right of the edge and darker to the left and when we apply the Dy it detects horizontal edges by giving highest gaussian value to pixels bellow the edge and smaller weight to those above.

   5. First Dx, then Gx^T
      Here the one dimensional gaussian filter is smoothing in the horizontal direction (in general filter the high frequency pixels) followed by a first order differentiation in y direction (Gx^T = Gy), which attributes highest gaussian values to pixels positioned right to the edges and low values to those in the left.

   6. First Gx^T , then Dx
      This combination has the same effect as question number five, because of the linear property of derivative and convolution operation.

1.e
With a kernel radius of 3 sigma and kernel size of (2 * kernel radius) + 1 this filter detects horizontal and vertical edges by applying a convolution operation between the image and Dy and Dx filter respectively, and also a diagonal gradient filter, which combines the horizontal and vertical gradient images in a square root form to detect diagonal edges.
Finally the horizontal and the vertical gradient filter have been applied to the images “graf.png” and “gantrycrane.png” to detect the vertical and horizontal edges respectively, and from the output of the gradient images we can clearly see that because of the derivative filter which amplifies abrupt transition in pixel intensity, the edges are emphasized and detected. More specifically horizontal edges are detected by vertical gradient filter and vertical edges are detected by horizontal gradient filter.
Before applying the gradient filters, it is very important to filter (smooth) the image first, that is because generally noises are overlapped to the signal (the image) and the gradient filter will not only amplify the edges but also the high frequency signals (noise) and introduces artefacts in the output image (aliasing), in this sense the filter can be considered as a low pass filter.

2. Image Representations, Histogram Distances (10 points)

3. Object Identification (10 points)

4. Performance Evaluation (bonus question for 10 points, not compulsory)