You will implement three keys functions of the KCF tracker, described in [[http://www.robots.ox.ac.uk/~joao/publications/henriques_tpami2015.pdf | High-Speed Tracking with Kernelized Correlation Filters]] by Henriques et.al.


====== How to start work ======
  - Download code [[ http://cmp.felk.cvut.cz/~mishkdmy/ws_ucu_2017/video_lab_3_task.zip| video_lab_3_task.zip ]]
  - unpack to $KCFDIR



====== Gaussian correlation ======
Write a function  ''function k = kernel_correlation(sigma, x, x_prime)'' ,
 which computes gaussian kernel with bandwidth sigma for all displacements between input patches X and X_prime, which must both be MxN, in Fourier domain.


{{:courses:ucuws17:labs:kcf_31.png?600|}}


''hat'' stands for Fourier-transformed patches, X∗ is the complex-conjugate (function ''conj'') of X, 
     
    
Functions ''fft2'' and ''circshift'' will help you. ''circshift'' will set of the response map in the center of the image after ''ifft2(fft2())'', ⨀ stands for element-wise multiplication


====== Training  ======
 {{:courses:ucuws17:labs:kcf_17.png?200|}}

Write function ''alphaf = train_kcf(x,yf,sigma,lambda)'', which computes filters values. ''yf'' comes already in Fourier domain, ''sigma'' is parameter for ''kernel_correlation'' and ''lambda'' is regularization parameter in Ridge regression. Division is element-wise. Output ''alphaf'' should be in Fourier domain.



====== Detection  ======
{{:courses:ucuws17:labs:kcf_19.png?200|}}

Write a function ''response_map = detect_kcf(x,z,sigma,alphaf)''. This function returns response map between patches X and Z, which must both be MxN, using alphaf weights. Convert response map to spatial domain by ''ifft2'' before returning.


Examples of tho two patches, their pixel-wise difference and response map are shown in figure below

{{:courses:ucuws17:labs:kcf_resp7.png?500|}}


After finishing this 3 functions, run ''run_tracker.m'' file to test tracker and save image output.