1. A motion vector detecting apparatus comprising: image receiving means including a frame memory for receiving and storing video image signals of two consecutive frames of picture elements; a subtracting circuit connected to said image receiving means for obtaining a difference signal representative of a difference value of respective picture elements at corresponding positions between said two frames; an absolute value circuit connected to said subtracting circuit for obtaining a residual difference signal formed of an absolute value of a signal output from said subtracting circuit, said signal output from said subtracting circuit representing the difference value of respective picture elements at corresponding positions between said two frames; a solution vector detecting circuit including a residual difference memory for dividing an output signal from said absolute value circuit representing the absolute value of the difference value of respective picture elements at corresponding positions between said two frames into a plurality of blocks of difference values of respective picture elements and for summing residual difference signals stored in said residual difference memory for each block and obtaining a solution vector of said block with one-picture-element pitch accuracy from a minimum value of the summed values; a predicting circuit for predicting an extreme value of a half-picture-element pitch in each of eight equally spaced directions by interpolating said residual difference signals in a vicinity of said solution vector of said one-picture-element pitch; a correction value circuit connected to said predicting circuit for detecting a minimum value of said extreme values and developing a correction value corresponding to said detected minimum value; and a vector signal generating circuit connected to said correction value circuit and to said solution vector detecting circuit for developing an output vector signal which is equal to said solution vector of said one-picture-element pitch added to said correction value.