For those wondering, the blue square is a "Dialog Power Management IC" according to ifixit, and the pink if for Wi-Fi.
Here's more information about the image processor.
An image processor, image processing engine, also called media processor, is a specialized digital signal processor (DSP) used for image processing in digital cameras, mobile phones or other devices. Image processors often employ parallel computing even with SIMD or MIMD technologies to increase speed and efficiency.
As one of the differences between GPU and DSP:
Graphics processing Unit or GPU is designed to accelerate creation of images for a computer display.
DSP is usually to measure, filter and/or compress continuous real-world analog signals.
What tasks does the fixed-function image/video processing hardware in modern systems do?
I think it should do jobs like encoding/decoding video. Because the codes used in video encoding/decoding are relatively fixed and have standard (e.g. H.264), we can use fixed-function hardware to process them and to gain speedup and save energy. I have done something with software encoding/decoding video, it is slower than hardware and needs more energy.