Hi i am a beginner in computer vision and i wish to know what exactly is the difference between a homography and affine tranformation, if you want to find the translation between two images which one would you use and why?.

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In geometry, an affine transformation, affine map or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line.

Common Names: Affine Transformation. In many imaging systems, detected images are subject to geometric distortion introduced by perspective irregularities wherein the position of the camera(s) with respect to the scene alters the apparent dimensions of the scene geometry. Applying an affine transformation to a uniformly distorted image can correct for a range of perspective distortions by transforming the measurements from the ideal coordinates to those actually used. For example, this is useful in satellite imaging where geometrically correct ground maps are desired. wherein a machine part is shown lying in a fronto-parallel plane. The circular hole of the part is imaged as a circle, and the parallelism and perpendicularity of lines in the real world are preserved in the image plane.

So, this class library implements affine transformations on images such as translation, rotation, scaling, schear. Algorithm isn't efficient but it's simple. puts source image pixels on destination image using tranformation Matrix with defined interpolation method. HOW? First of all we need to find reverse transformation to the defined. WHY? If you transform pixels of source bitmap using defined matrix and put them on destination bitmap, an output image may have "holes". Just imagine the easiest transformation like 2x scaling: Solution on that problem is transforming in opposite direction.

We mentioned that an Affine Transformation is basically a relation between two images. If we find the Affine Transformation with these 3 points (you can choose them as you like), then we can apply this found relation to all the pixels in an image.

In geometry, an affine transformation, affine map or an affinity is a function between affine spaces which preserves points, straight lines and planes.

In other words, an affine transformation combines a linear transformation with a translation. Quite obviously, every linear transformation is affine (just set to the zero vector). However, not every affine transformation is linear. The previous section defined affine transformation . the concept of affine space, and now it's time to pay the rigor debt. is a geometric structure that generalizes the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

An affine transformation has fewer rules, it no longer needs to preserve the origin it just has to keep straight lines straight and some other stuff. Affine operations like ‘rotate and translate’ are pretty useful and it would be helpful we could express them as a single matrix multiplication (Ax) instead of a multiplication and a vector addition (Ax + b). It turns out that affine transformations in 2D can be represented as linear transformations in 3D. First let’s hoist our 2D space into 3D by making it a plane at z 1. Notice the old origin is now at (0,0,1) in our 3D space.