1. An image processing apparatus, comprising: an image obtaining device that obtains a first image and a second image; a hierarchical tier image creating device that creates a first hierarchical tier image group including a plurality of first hierarchical tier images with different resolutions by subjecting the first image to stepwise reduction processing, and creates a second hierarchical tier image group including a plurality of second hierarchical tier images with different resolutions by subjecting the second image to stepwise reduction processing; a tracking point detecting device that detects a position of a tracking point in a second hierarchical tier image with a predetermined resolution in the second hierarchical tier image group, the tracking point corresponding to a predetermined feature point in a first hierarchical tier image with the predetermined resolution in the first hierarchical tier image group, based on a gradient of an image signal in each of the first and second hierarchical tier images; and a sequential detection device that performs the tracking point detection by the tracking point detecting device for hierarchical tier images included in each of the first and second hierarchical tier image groups in increasing order of resolution while reflecting the result of tracking point detection in a hierarchical tier image with a lower resolution, to detect a position of a tracking point in the second image, the tracking point corresponding to a feature point in the first image, wherein the tracking point detecting device includes: a displacement calculating device that repeatedly detects a position of a tracking point in a second hierarchical tier image with a predetermined resolution in the second hierarchical tier image group, the tracking point corresponding to a predetermined feature point in a first hierarchical tier image with the predetermined resolution in the first hierarchical tier image group, based on a gradient of an image signal in each of the first and second hierarchical tier images, and calculates a displacement amount representing a distance between a latest tracking point detected as a result of a detection repetition and a tracking point obtained as a result of a detection repetition before the detection repetition in the second image; a detection result outputting device that stops the repetitive tracking point detection by the displacement calculating device when the displacement amount converges on a value of less than a first threshold value or the repetition count of the tracking point position detection reaches not less than a second threshold value, and outputs a value of each of the displacement amount and the repetition count for the point of time of stopping the repetitive detection; and a criterion setting device that sets the first threshold value for the case where the tracking point detection by the tracking point detecting device is performed for the first and second hierarchical tier images in the first and second hierarchical tier image groups, respectively, the first and second hierarchical tier images having a second resolution that is higher than the first resolution, according to the value of each of the displacement amount and the repetition count output from the detection result outputting device.