1. A line-of-sight detection device comprising: a memory configured to store an image of a person that includes eyes of the person; and a processor configured to detect a line of sight of the person on the basis of the image stored in the memory, wherein the detecting the line of sight of the person includes: extracting a candidate corneal reflection having a specified feature from a first image and from a second image captured after the first image is captured; extracting a reference point on the person from the first image and from the second image; calculating a threshold vector on the basis of a movement vector of the reference point and a predetermined threshold, wherein the movement vector has a start point at a location, in the second image, that overlaps the reference point in the first image and an endpoint at the reference point in the second image, and the threshold vector has a start point at a candidate location, in the second image, that overlaps a location of the candidate corneal reflection in the first image; calculating a movement vector of a reflection location that has a start point at the candidate location in the second image and an endpoint at a location of the candidate corneal reflection extracted from the second image, and identifying, on the basis of the threshold vector and the movement vector of the reflection location, a corneal reflection from among a plurality of candidate corneal reflections extracted from the second image so as to identify a location of the corneal reflection; extracting a location of a pupil from the image; and calculating the line of sight of the person in the image on the basis of the identified location of the corneal reflection and the extracted location of the pupil.