1. A lane recognition device which recognizes a lane on the basis of a captured image of a view ahead of a vehicle obtained by an imaging device, comprising: a linear element extraction image generating unit which generates a linear element extraction image into which linear elements included in the captured image have been extracted; an area setting unit which sets a lane extraction area in a predetermined range in a vertical direction in the linear element extraction image; a local straight line determining unit which determines a local straight line of each local area on the basis of a linear element part in each local area with respect to each local area in the lane extraction area; an intersection calculating unit which calculates an intersection of each local straight line and a reference horizontal line at a predetermined position in a vertical direction; a voting unit which votes on a direction and an intersection of each local straight line in a voting space having a direction and an intersection as coordinate components; a detecting unit which detects a detection straight line on the basis of a voting result in the voting space; and a recognizing unit which recognizes a lane boundary line based on the detection straight line, wherein the area setting unit divides the linear element extraction image into a plurality of lane extraction areas in the vertical direction, the voting unit casts a vote to each voting space associated with each lane extraction area on the basis of each local straight line of the lane extraction area associated with the voting space, the detecting unit detects the detection straight line for each lane extraction area on the basis of the voting result of each voting space, the recognizing unit recognizes a lane boundary line in the linear element extraction image on the basis of connected detection straight lines of each lane extraction area, the local straight line determining unit divides a direction of a predetermined range into a first predetermined number of directional sections and determines the direction of each local straight line by assigning the direction of each local straight line to a corresponding directional section, the intersection calculating unit divides the reference horizontal line into a second predetermined number of positional sections and determines the intersection of each local straight line and the reference horizontal line by assigning the intersection to an intersectional section serving as a corresponding positional section, and the voting unit makes coordinate components of a direction and an intersection defined in the voting space coincide with the directional section and the intersectional section.