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This paper studies weakly supervised learning on spatial raster data based on imperfect vector training labels. Given raster feature imagery and imperfect (weak) vector labels with location registration errors, our goal is to learn a deep learning model for pixel classification and refine vector labels simultaneously. The problem is important in many geoscience applications such as streamline delineation and road mapping from earth imagery, where annotating imperfect coarse vector labels is far more efficient than drawing precise labels. But the problem is challenging due to the misalignment of vector labels with raster feature pixels and the need to infer true vector label location while learning neural network parameters. Existing works on weakly supervised learning often focus on noise and errors in label semantics, assuming label locations to be either correct or irrelevant (e.g., identical and independently distributed). A few works exist on label registration errors, but these methods often focus on label misalignment on object segment boundaries at the pixel level without guaranteeing vector continuity. To fill the gap, this paper proposes a spatial learning framework based on Expectation-Maximization that iteratively updates deep neural network parameters while inferring true vector label locations. Specifically, inference of true vector locations is based on both the current pixel class predictions and the geometric properties of vectors. Evaluations on real-world high-resolution remote sensing datasets in National Hydrography Dataset (NHD) refinement show that the proposed framework outperforms baseline methods in classification accuracy and refined vector quality.

In recent years, deep learning techniques (e.g., U-Net, DeepLab) have achieved tremendous success in image segmentation. The performance of these models heavily relies on high-quality ground truth segment labels. Unfortunately, in many real-world problems, ground truth segment labels often have geometric annotation errors due to manual annotation mistakes, GPS errors, or visually interpreting background imagery at a coarse resolution. Such location errors will significantly impact the training performance of existing deep learning algorithms. Existing research on label errors either models ground truth errors in label semantics (assuming label locations to be correct) or models label location errors with simple square patch shifting. These methods cannot fully incorporate the geometric properties of label location errors. To fill the gap, this paper proposes a generic learning framework based on the EM algorithm to update deep learning model parameters and infer hidden true label locations simultaneously. Evaluations on a real-world hydrological dataset in the streamline refinement application show that the proposed framework outperforms baseline methods in classification accuracy (reducing the number of false positives by 67% and reducing the number of false negatives by 55%).

A method and device for segmenting an electric (acoustic) signal. A number of parameters, for example "log area" parameters, are derived as a function of time from the electric signal (block 2). For consecutive instants the signals of the parameters located within a time interval around each instant are taken up and transition functions (.0. i ) are derived therefrom for each instant (block 3). Subsequently similarity factors (c ij ) are determined each between two transition functions (.0. i and .0. j ) associated with respective proximate instants (i and j) (block 4) and a replacing transition function (.0. ij c ) is derived (block 6) from the transition functions of at least one group of two transition functions for which the associated similarity factor is larger than a reference value V, the transition function (.0. ij c ) replace the aforementioned transition functions from which it is derived (block 7). A combined transition function (.0. ij c ) replacing one of these transition functions is preferably calculated from the aforementioned transition functions, while the other of these transition functions are omitted. The group of transition functions for which the similarity factor is largest is preferably taken (block 5). The method is subsequently repeated (FIG. 1). Transition functions obtained are very suitable for use in the transmission or recognition of speech signals and for coding diphones.