1. An image processing device comprising: an estimating portion that estimates, based on first image data obtained through imaging, using an imaging device, a first image that includes a specific image pattern, and based on second image data obtained by imaging, using the imaging device, a second image that does not include the specific image pattern, a frequency component of noise that is included in both the first and second images, and a frequency component of a first image that does not include the noise; and a controlling portion that controls weightings, relative to frequencies, when calculating a correlation between the first image data and third image data, obtained through imaging a third image through the imaging device, based on the individual frequency components estimated by the estimating portion, wherein the estimating portion comprises a first frequency component analyzing portion that analyzes a frequency component of the first image data, a second frequency component analyzing portion that analyzes a frequency component of the second image data, and a subtracting portion that subtracts the analysis result by the second frequency component analyzing portion from the analysis result by the first frequency component analyzing portion, wherein the controlling portion controls the weighting based on the subtracting result by the subtracting portion and on the analysis result by the second frequency component analyzing portion, wherein the first and the second frequency component analyzing portions each comprise a band limiting portion that applies a variable-frequency band limiting process to the input image data; and a sum-of-squares calculating portion that calculates a sum of squares of a band limiting result by the band limiting portion, wherein the control of the weightings by the controlling portion selects a maximum frequency wherein a ratio of the sum-of-squares result by the sum-of-squares calculating portion exceeds a specific threshold value as a reference frequency for the band limiting process that is performed in the process of calculating a frequency-weighted correlation of the first and third image data.