1. A vehicle periphery monitoring device which is provided with an imaging unit mounted in a vehicle to image a periphery of the vehicle and is configured to monitor the periphery of the vehicle on the basis of a captured image by the imaging unit, comprising: an object detecting portion configured to detect a distance from the vehicle of an object located in an imaging area imaged by the imaging unit; an image processing target area setting portion configured to set an image processing target area which may include an image portion of a monitoring object in the captured image on the basis of the detected distance of the object from the vehicle by the object detecting portion; a contour extracting portion configured to extract a contour of the image portion included in the image processing target area; and an object type discriminating portion configured to discriminate a type of the monitoring object in a real space corresponding to the image portion from which the contour has been extracted by the contour extracting portion on the basis of the extracted contour, wherein the contour extracting portion extracts the contour of the image portion by setting an initial eclipse circling the image portion in the image processing target area and performing a contour convergence processing on the initial ellipse according to Snakes algorithm, the contour convergence processing is performed according to the Snakes algorithm by using a computation expression in which a multiplication term of an internal energy of Snakes energy where the Snakes energy and a contour positional variation and an external energy variation and an internal energy variation are presumed to be of zero at the time when a contour of a Snakes model of a discrete system is converged is multiplied to a multiplication term of the external energy, and wherein the contour extracting portion uses the following mathematical expressions (1) and (2) as the computation expression: 
 [Mathematical expression 1] 
 x t =( I−gA ){ x t-1 −gf x ( x t-1 ,y t-1 )}  (1) 
 [Mathematical expression 2] 
 y t =( I−gA ){ y t-1 −gf y ( x t-1 ,y t-1 )}  (2) Herein, (x t , y t ): coordinate of a contour dot at timing t; (x t-1 , y t-1 ): a model expression of the contour at timing t−1; I: a unit matrix; A: a transform matrix of internal energy: γ: an iteration step (moving amount of the contour per step when converged inward); f x : a computation expression of x components of the external energy; and f y : a computation expression of y components of the external energy.