Useful Materials Distinctive Image Features from Scale-Invariant Keypoints[1] by David G. Lowe. SIFT(Scale-Invariant Feature Transform)[2] on Towards Data Science. The SIFT (Scale Invariant Feature Transform) Detector and Descriptor[3]. Notes Uses DoG (Difference of Gaussian) to approximate Scale-normalized LoG (Laplacian of Gaussian)[4]. where is the two dimensions Gaussian function, and is the input image. [need more consideration] After each octave, the Gaussian image is down-sampled by a factor of 2, by resampling the Gaussian image that has twice the initial value of by taking every second pixel in each row and column. And we start on the new octave with . Since the image size is reduced to 1/4, the sigma for the next octave becomes , which is equal to . To understand it, frist consider this question: If the image size is reduced to 1\4, but the kernel size of

Types of Noise Additive noise Additive noise is independent from image signal. The image g with nosie can be considered as the sum of ideal image f and noise n.[1] Multiplicative noise Multifplicative noise is often dependent on image signal. The relation of image and noise is[1]: Gaussian noise Gaussian noise, named after Carl Friedrich Gauss, is statistical noise having a probability density function (PDF) equal to that of the normal distribution, aka. the Gaussian distribution. i.e. the values that the noise can take on are Gaussian-distributed. The PDF of a Gaussian random variable is given by[2]: Salt-and-pepper noise Fat-tail distributed or "impulsive" noise is sometimes called salt-and-pepper nosie or spike noise. An image containing salt-and-pepper noise will have dark pixels in bright regions and bright pixels in dark regions.[2] The PDF of (Bipolar) Impulse noise is given by: if b > a, gray