We present “conversational image editing”, a novel real-world application domain combining dialogue, visual information, and the use of computer vision. We discuss the importance of dialogue incrementality in this task, and build various models for incremental intent identification based on deep learning and traditional classification algorithms. We show how our model based on convolutional neural networks outperforms models based on random forests, long short-term memory networks, and conditional random fields. By training embeddings based on image-related dialogue corpora, we outperform pre-trained out-of-the-box embeddings, for intention identification tasks. Our experiments also provide evidence that incremental intent processing may be more efficient for the user and could save time in accomplishing tasks.