Is programmatically inverting the colors of an image possible?

Swift 3 update: (from @BadPirate Answer)

extension UIImage {
func inverseImage(cgResult: Bool) -> UIImage? {
    let coreImage = UIKit.CIImage(image: self)
    guard let filter = CIFilter(name: "CIColorInvert") else { return nil }
    filter.setValue(coreImage, forKey: kCIInputImageKey)
    guard let result = filter.value(forKey: kCIOutputImageKey) as? UIKit.CIImage else { return nil }
    if cgResult { // I've found that UIImage's that are based on CIImages don't work with a lot of calls properly
        return UIImage(cgImage: CIContext(options: nil).createCGImage(result, from: result.extent)!)
    }
    return UIImage(ciImage: result)
  }
}

To expand on quixoto's answer and because I have relevant source code from a project of my own, if you were to need to drop to on-CPU pixel manipulation then the following, which I've added exposition to, should do the trick:

@implementation UIImage (NegativeImage)

- (UIImage *)negativeImage
{
    // get width and height as integers, since we'll be using them as
    // array subscripts, etc, and this'll save a whole lot of casting
    CGSize size = self.size;
    int width = size.width;
    int height = size.height;

    // Create a suitable RGB+alpha bitmap context in BGRA colour space
    CGColorSpaceRef colourSpace = CGColorSpaceCreateDeviceRGB();
    unsigned char *memoryPool = (unsigned char *)calloc(width*height*4, 1);
    CGContextRef context = CGBitmapContextCreate(memoryPool, width, height, 8, width * 4, colourSpace, kCGBitmapByteOrder32Big | kCGImageAlphaPremultipliedLast);
    CGColorSpaceRelease(colourSpace);

    // draw the current image to the newly created context
    CGContextDrawImage(context, CGRectMake(0, 0, width, height), [self CGImage]);

    // run through every pixel, a scan line at a time...
    for(int y = 0; y < height; y++)
    {
        // get a pointer to the start of this scan line
        unsigned char *linePointer = &memoryPool[y * width * 4];

        // step through the pixels one by one...
        for(int x = 0; x < width; x++)
        {
            // get RGB values. We're dealing with premultiplied alpha
            // here, so we need to divide by the alpha channel (if it
            // isn't zero, of course) to get uninflected RGB. We
            // multiply by 255 to keep precision while still using
            // integers
            int r, g, b; 
            if(linePointer[3])
            {
                r = linePointer[0] * 255 / linePointer[3];
                g = linePointer[1] * 255 / linePointer[3];
                b = linePointer[2] * 255 / linePointer[3];
            }
            else
                r = g = b = 0;

            // perform the colour inversion
            r = 255 - r;
            g = 255 - g;
            b = 255 - b;

            // multiply by alpha again, divide by 255 to undo the
            // scaling before, store the new values and advance
            // the pointer we're reading pixel data from
            linePointer[0] = r * linePointer[3] / 255;
            linePointer[1] = g * linePointer[3] / 255;
            linePointer[2] = b * linePointer[3] / 255;
            linePointer += 4;
        }
    }

    // get a CG image from the context, wrap that into a
    // UIImage
    CGImageRef cgImage = CGBitmapContextCreateImage(context);
    UIImage *returnImage = [UIImage imageWithCGImage:cgImage];

    // clean up
    CGImageRelease(cgImage);
    CGContextRelease(context);
    free(memoryPool);

    // and return
    return returnImage;
}

@end

So that adds a category method to UIImage that:

1. creates a clear CoreGraphics bitmap context that it can access the memory of
2. draws the UIImage to it
3. runs through every pixel, converting from premultiplied alpha to uninflected RGB, inverting each channel separately, multiplying by alpha again and storing back
4. gets an image from the context and wraps it into a UIImage
5. cleans up after itself, and returns the UIImage

Sure, it's possible-- one way is using the "difference" blend mode (kCGBlendModeDifference). See this question (among others) for the outline of the code to set up the image processing. Use your image as the bottom (base) image, and then draw a pure white bitmap on top of it.

You can also do the per-pixel operation manually by getting the CGImageRef and drawing it into a bitmap context, and then looping over the pixels in the bitmap context.

With CoreImage:

#import <CoreImage/CoreImage.h>

@implementation UIImage (ColorInverse)

+ (UIImage *)inverseColor:(UIImage *)image {
    CIImage *coreImage = [CIImage imageWithCGImage:image.CGImage];
    CIFilter *filter = [CIFilter filterWithName:@"CIColorInvert"];
    [filter setValue:coreImage forKey:kCIInputImageKey];
    CIImage *result = [filter valueForKey:kCIOutputImageKey];
    return [UIImage imageWithCIImage:result];
}

@end