1. An image processing apparatus comprising: a processor; an obtaining unit, executed on the processor, that obtains original image data representing a color of each pixel included in an image; a dividing unit that divides the image represented by the original image data obtained by the obtaining unit into a plurality of image regions through a labeling process; a low-resolution image data generation unit that generates low-resolution image data representing the image at a lower resolution than the resolution of the original image data; a first determination unit that determines whether each of the image regions divided by the dividing unit is an image region for a vector image, based on a characteristic amount of the image represented by the low-resolution image data generated by the low-resolution image data generation unit, the vector image being an image where the process for rendering the image is defined by numerical values or numerical formulas; a color number counting unit that, in a case where the first determination unit has determined that the image region is an image region for a vector image, counts the number of colors in the pixels of high-resolution image data representing the image included in the image region, the high-resolution image data having a resolution that is higher than the low-resolution image data; a frequency counting unit that, in a case where the first determination unit has determined that the image region is an image region for a vector image, counts a number of times where the difference between the colors of each of the pixels in the high-resolution image data and the colors of at least one pixel located around each of those pixels is greater than or equal to a first threshold; a second determination unit that, in a case where at least one of the number counted by the color number counting unit and the number of times counted by the frequency counting unit in the image region determined by the first determination unit to be an image region for a vector image is greater than a second threshold, determines that the image region is not an image region for a vector image; and a generation unit that generates image data in which a process for rendering images in the image regions determined by the first determination unit to be image regions for vector images, but excluding the image regions determined by the second determination unit to not be image regions for vector images, is defined by numerical values or numerical formulas.