in digital signal processing, quantization is the step of converting a signal's real-valued samples into a finite string of bits. as the first step in digital processing, it plays a crucial role in determining the information conversion rate and the reconstruction accuracy. compared to non-adaptive quantizers, the adaptive ones are known to be more efficient in quantizing bandlimited signals, especially when the bit-budget is small (e.g.,1 bit) and noises are present. however, adaptive quantizers are currently only designed for 1d functions/signals. in this talk, i will discuss challenges in extending it to high dimensions and present our proposed solutions. specifically, we design new adaptive quantization schemes to quantize images/videos as well as functions defined on 2d surface manifolds and general graphs, which are common objects in signal processing and machine learning. mathematically, we start from the 1d sigma-delta quantization, extend them to high-dimensions and build suitable decoders. the discussed theory would be useful in natural image acquisition, medical imaging, 3d printing, and graph embedding.