Plastic is being produced at an ever-increasing rate, mostly for short-lived products that end up polluting the environment. Bioplastics and recycling can play an important role in mitigating this problem. Improving the speed and/or accuracy of plastic sorting mechanisms is imperative. In this paper, the detection of plastic objects using instance segmentation and hyperspectral imaging is explored. State-of-the-art instance segmentation model Mask R-CNN is used, with 30 hyperspectral images of PE, PP and PET flakes as input. These types of models are typically used for regular RGB images, so dimensionality reduction is required. This dimensionality reduction of the images is done by an added convolutional layer that precedes the Mask R-CNN model. Excluding outliers, the average result over 20 runs of 100 epochs is an instance segmentation mask mAP (IoU 0.5:0.95) of 0.8261. Including outliers, mAP is 0.7057. Interestingly, adding a second convolutional layer for dimensionality reduction does not lead to improved results. A positive finding is that using hyper-hue dimensions, the output of pre-processing step HHSI, appears to work well as a way of separating the three plastics. Future research could shed light on the relation between hyper-hue dimensions and spectral bands. The hyperspectral bands that contribute the most to the dimensionality reduction process, appear to be the ones that show large absolute differences in average relative reflection between the three plastics. Overall, this paper shows that hyperspectral images in combination with instance segmentation framework Mask R-CNN and the use of a convolutional layer for dimensionality reduction work well for detecting different types of plastic flakes. Several aspects, such as the use of convolutional neural networks for dimensionality reduction, deserve further study.