Chronic wounds are a significant health concern, encompassing their various types such as diabetic foot ulcers, venous ulcers, and pressure injuries. Their effective management requires a systematic and objective diagnostic and therapeutic approach. In this paper, we present a machine learning-based approach for the detection and segmentation of chronic wounds using multimodal image data. Our system exploits the integration of RGB and thermal images to provide a comprehensive assessment of wound characteristics. The key contributions of our work include the development of a semantic segmentation process and a deep machine learning algorithm for the detection and segmentation of chronic wounds in multimodal images. The results, obtained over a multimodal chronic wound benchmark following a multi-fold cross-validation strategy, show that SegNet models are effective in image classification, particularly in identifying negative cases, with the mean (median) specificity of up to 0.993 (0.994) for RGB images. Also, our experiments indicated that SegNets substantially outperform U-Nets while segmenting chronic wounds, with the mean (median) Dice Index of 0.612 (0.633) and 0.413 (0.474) for SegNet and U-Net, respectively.