1. A motion estimation system comprising: an initializing circuit generating first and second initial motion fields by allocating an initial motion vector to each block of a first motion field related to a first motion change of an image which accompanies a change from an (n−1)-th frame to an n-th frame and to each block of a second motion field related to a second motion change of the image which accompanies a change from the n-th frame to the (n−1)-th frame; a candidate test circuit generating first and second random motion fields by comparing a similarity function value of the initial motion vector allocated to each block of each of the first and second initial motion fields with a similarity function value of a random motion vector, generating first and second spatial propagation motion fields by comparing a similarity function value of a motion vector allocated to each block of each of the first and second random motion fields with similarity function values of motion vectors allocated to adjacent blocks, and generating first and second optimum motion fields by comparing a similarity function value of a motion vector allocated to each block of the first spatial propagation motion field with a similarity function value of a motion vector allocated to each block of the second spatial propagation motion field; a random candidate searching circuit comparing the similarity function value of the initial motion vector allocated to each block of each of the first and second initial motion fields with the similarity function value of the random motion vector and generating the first and second random motion fields in which a motion vector with a smaller similarity function value among the initial motion vector and the random motion vector is allocated to each block; a temporal propagation circuit comparing the similarity function value of the motion vector allocated to each block of the first spatial propagation motion field with the similarity function value of the motion vector allocated to each block of the second spatial propagation motion field and generating the first and second optimum motion fields in which a motion vector with a smaller similarity function value among the motion vectors is allocated to each block; and an upscaling circuit which receives the first and second optimum motion fields from the temporal propagation circuit, upscales the first and second optimum motion fields, and provides the upscaled first and second optimum motion fields to the random candidate searching circuit as the first and second initial motion fields.