An Ideal point is a point in infinity,it has a 0 in the z coordinate and we can not divide by 0, the problem we have therefore is that the ray that defines it, is parallel to the image plane, and doesn’t intersect with it. On the other hand, theContinue Reading
A line projected on the image space, is defined by the plane formed by the rays intersecting with the image space, and that plane is defined (mathematically) by a normal(perpendicular line) in projective space. Line on the image is defined by the normal to the plane: Basically: The Formula isContinue Reading
Given a projection matrix m, it’s null space is the camera center. Why? Because every point on a specific ray that is projected through projection line of the camera center has to land on the same spot on the image, so that means that the camera matrix times the center point mustContinue Reading
Every rigid body has 6DOF potential in 3D space. One point has to be fixed to an x,y,z location – so that holds the first 3 DOF. The vector from it to any given point in the rigid object has to be constant in the z axis – because theContinue Reading
Similarity – pixels should look alike (image patch on the left should look like the image patch on the right). Assumptions: Most scene points visible in both views. Image regions for matches are similar in appearance. Tactics- Do a dense correspondence by first: Normalize images to same standard deviation ofContinue Reading
Transforming a signal from a function of time or space to frequency(ω) which holds within it’s unique (ω) key also the respected phase(φ) and a respected amplitude/magnitude (A), is called a fourier transform. This is possible because any signal can be represented as a sum of sinusoids. f(x) –> TransformContinue Reading
A displacement vector is a vector whose length is the shortest distance from the initial to the final position of an object: s= xf-xi = Δx Hough-R(r)-Table: 1: Compute r (instead of s but basically the same): r= c(center of object) – p(i)(point number i) 2:measure the gradient angle θContinue Reading
Circle equation = (x-a) ²+ (y-b)²= r² (a,b is the center and r is the radius) Circle Hough Space is represented using a as the horizontal axis and b as the vertical axis. Each point from x,y is represented in hough space using its a,b as center of the circle,Continue Reading
Formula of the line is: xcos(θ ) – ysin(θ ) = d d(distance) = Perpendicular distance from origin(reference point) to a line. θ(angle) = Angle of the perpendicular line makes with the x axis (reference direction). Continue Reading
Examples of parametric models are: lines / circles/ arbitrary shapes/templates. As an easy example: Line. Line model has three requirements: 1. how many lines are there? 2. which points combine which line? 3. what is the line? Parametric models use voting systems to fill in occlusions and cancel noisy lines,Continue Reading
Yair Shinar for Clarity and Solutions