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CSC320 TT1 (2D Image - 2D Patches & Curves (essentially the same,…

- - - - could use gradient length, or just absolute value(manhattan distance)
    - - partial derivative x
        
        for sky, its mostly gray, very significant change along x edges
      - partial derivative y
        
        for sky, its mostly gray, very significant change along y edges
      - gradient length
        
        mostly black for sky (since no typical variation), strong for wires(I think the black could manually lowered, it should be consistent with partial x and y's magnitude, since it's 2-norm of df/dx and df/dy.)
        
        filtered(threshholded length) has discontinuity
      - angle: looks like aluminum foil
      - Edge Detection: first attempt: distinguish edges by gradient length(change in magnitude)
        
        But image have a lot of noise!
        
        smooth it before solving for gradient: Kernel
        
        Q: do we smooth it when using RANSAC? using polynomial ine fitting? Where do they intersect?
        
        apply convolution(exactly same as CC right now: kernal is symmeric)
        
        Sobel/Averaging filter (take average)
        
        BUT even with good threshhold, still not single pixel for gradient peak! (instead a relatively wide interval)
        
        Second Attempt Idea: find it with 2-nd derivative then! (zero-crossing)
        
        In 2D the derivative is called Laplacian(note: a scalar!) dot product/inner product
        
        same thing, apply Gaussian filter first(the normal kernel, or 2mid +left+right/4 ??)
        
        as Gaussian increase in standard deviation(variance, range of values taken in from), the resulting graph has a less sharp, more continuous look, also a lot of the points are diluted out, overall more sparse
        
        1 more item...
        
        Canny Edge Algorithm: Step 1: Filter with derivative of Gaussian(Why derivative? I think he combines Gaussian and derivative, BUT Shouldn't it be Laplacian??) Step 2: Calculate magnitude and orientation(angle) of resulting gradient Step 3: Thin out thick edges . Step 4: Hysteresis Thresholding: (detect weaker edges)
        
        Step 3: Non-maxima suppression - compare gradients along +/-, that's where an edge could happen, locate the region and pick a peak as single response
        
        Ideal Edge Detector: Good Detection & Localization, Single Response
- - - - sample 2w+1 pixels in a patch
        
        RANSAC
        
        more robust: model poly only for some pixels in a patch, rather than trying to please every pixel in that patch
        
        n=degree of poly, p=fraction of inliers, t=fit threshhold (t determines p?) p_s = success probability(can be calculated?)
        
        question, if n=2, which means we take two points secant line, wouldn't that be a linear line? But by definition it is a 2-degree poly??? Or means unknown polynomial coefficients? (that would degree it by one degree)
        
        algorithm: Step 1: pick n points from patch randomly Step 2: fit poly lines Step 3: see how many points in the patch are within the threshhold Step 4: Repeat if there are not enough points under threshhold for the polynomial fit found for the n points chosen
        not more than K times iteraitons(pre-set)
        Step 4: success case: STOP, label those points in the patch as inliers(for that patch/sliding frame), do a least-square fit to the inliers ONLY
        
        essentially RANSAC just prefilters with a customized degree(usually we pick two points), then we can actually compute the square fit to the inliers, the values should be very similar
        
        least-mean-square
        
        fit linear system into intensities at different delta t, different input x,y as delta from original centre, and derivative as x in Ax=b, actual intensities as the vector b
        
        with weight assigning in a diagonal matrix applied to both sides