If you want to crop the image without changing its quality in Objective-c/cocoa (OSX) then you can use the following method

-(IBAction)crop:(id)sender{
    hasBeenDragged = NO;
    NSImage *_sourceImage = [self image];
    float width = selectedArea.size.width;
    float height = selectedArea.size.height;
    float xPos = selectedArea.origin.x;
    float yPos = selectedArea.origin.y;
    float centerX = ([self frame].size.width/2)-width/2;
    float centerY = ([self frame].size.height/2)-height/2;
    NSImage *_alteredImage = [[NSImage alloc]initWithSize:[_sourceImage size]];
    [_alteredImage lockFocus];
    [_sourceImage drawAtPoint:NSMakePoint(centerX,centerY) fromRect:NSMakeRect(xPos, yPos, width, height+50) operation:NSCompositeSourceOver fraction:1.0];
    [_alteredImage unlockFocus];
    [self setImage:_alteredImage];
    [self setNeedsDisplay:YES];
}