Optical Music Recognition (OMR) is an important and challenging area within music information retrieval, the accurate detection of music symbols in digital images is a core functionality of any OMR pipeline. In this paper, we introduce a novel object detection method, based on synthetic energy maps and the watershed transform, called Deep Watershed Detector (DWD). Our method is specifically tailored to deal with high resolution images that contain a large number of very small objects and is therefore able to process full pages of written music. We present state-of-the-art detection results of common music symbols and show DWD's ability to work with synthetic scores equally well as on handwritten music.
Most contemporary approaches to instance segmentation use complex pipelines involving conditional random fields, recurrent neural networks, object proposals, or template matching schemes. In this paper, we present a simple yet powerful end-to-end convolutional neural network to tackle this task. Our approach combines intuitions from the classical watershed transform and modern deep learning to produce an energy map of the image where object instances are unambiguously represented as energy basins. We then perform a cut at a single energy level to directly yield connected components corresponding to object instances. Our model achieves more than double the performance over the state-of-the-art on the challenging Cityscapes Instance Level Segmentation task. Image segmentation by mathematical morphology is a methodology based upon the notions of watershed and homotopy modification. This paper aims at introducing this methodology through various examples of segmentation in materials sciences, electron microscopy and scene analysis. First, we define our basic tool, the watershed transform. We show that this transformation can be built by implementing a flooding process on a grey-tone image. This flooding process can be performed by using elementary morphological operations such as geodesic skeleton and reconstruction. Other algorithms are also briefly presented (arrows representation). Then, the use of this transformation for image segmentation purposes is discussed. The application of the watershed transform to gradient images and the problems raised by over-segmentation are emphasized. This leads, in the third part, to the introduction of a general methodology for segmentation, based on the definition of markers and on a transformation called homotopy modification. This complex tool is defined in detail and various types of implementation are given. Many examples of segmentation are presented. These examples are taken from various fields : transmission electron microscopy, SEM, 3D holographic pictures, radiography, non destructive control and so on. The final part of this paper is devoted to the use of the watershed transformation for hierarchical segmentation. This tool is particularly efficient for defining different levels of segmentation starting from a graph representation of the images based on the mosaic image transform. This approach will be explained by means of examples in industrial vision and scene analysis.