1. A pixel interpolation processing apparatus for performing pixel interpolation processing on an image obtained by imaging circuitry having a four-color filter array in which, in an odd-numbered row, first-color component filters and second-color component filters are arranged alternately with a first-color component filter leading the row, and, in an even-numbered row, third-color component filters and fourth-color component filters are arranged alternately with a third-color component filter leading the row, the apparatus comprising: correlation value calculation circuitry configured to use pixel data for a surrounding area around a target pixel to obtain a plurality of sets of correlation values in two directions orthogonal to each other in the image; correlation direction determination circuitry configured to determine a correlation direction in the surrounding area around the target pixel based on the correlation values obtained by the correlation value calculation circuitry; and interpolation circuitry configured to perform the pixel interpolation processing on the target pixel based on the correlation direction determined by the correlation direction determination circuitry, wherein, when it is determined, based on the correlation values, that there is a direction with a high correlation, (1) if a color component value for the same color as that of a pixel located adjacent to the target pixel in the correlation direction is to be calculated, the interpolation circuitry selects a plurality of pixels that include the target pixel, have the same color, and are arranged in the correlation direction, and calculates a color component value for the same color as that of a pixel located adjacent to the target pixel in the correlation direction based on (i) pixel values of two pixels located adjacent to and sandwiching the target pixel in the correlation direction and (ii) a ratio of change in the correlation direction calculated using pixel values of the plurality of pixels that the interpolation circuitry has selected, (2) if a color component value for the same color as that of a pixel located adjacent to the target pixel in a normal direction which is a direction orthogonal to the correlation direction is to be calculated, the interpolation circuitry selects a plurality of pixels that have the same color and are arranged in the normal direction and calculates a color component value for the same color as that of a pixel located adjacent to the target pixel in the normal direction based on a ratio of change in the normal direction calculated using pixel values of two pixels included in the plurality of pixels that the interpolation circuitry has selected, the two pixels sandwiching the target pixel, and, (3) if a color component value for a first calculation target color which is a color component value having the same color as that of a pixel located adjacent to the target pixel in a direction inclined relative to the correlation direction is to be calculated, (3A) the interpolation circuitry selects a plurality of pixels with the same color from a first group of pixels which are a plurality of pixels including a first adjacent pixel that is one of pixels that are located adjacent to the target pixel in the normal direction and are arranged in the correlation direction, calculates a ratio of change in the normal direction from pixel values of the selected pixels, selects, from the first group of pixels, a pixel with the same color as the first calculation target color, and calculates a color component value for the first calculation target color of the first adjacent pixel based on the selected pixel and the calculated ratio of change in the normal direction, (3B) the interpolation circuitry selects a plurality of pixels with the same color from a second group of pixels which are a plurality of pixels including a second adjacent pixel that is another one of the pixels that are located adjacent to the target pixel in the normal direction and are arranged in the correlation direction, calculates a ratio of change in the normal direction from pixel values of the selected pixels, selects, from the second group of pixels, a pixel with the same color as the first calculation target color, and calculates a color component value for the first calculation target color of the second adjacent pixel based on the selected pixel and the calculated ratio of change in the normal direction, and (3C) the interpolation circuitry selects a plurality of pixels that have the same color and are arranged in the normal direction, calculates a ratio of change in the normal direction from pixel values of the selected pixels, and calculates a color component value for the first calculation target color of the target pixel based on (i) the calculated ratio of change in the normal direction, (ii) the calculated color component value for the first calculation target color of the first adjacent pixel, and (iii) the calculated color component value for the first calculation target color of the second adjacent pixel.