Abstract-In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (that is, SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV gray-level morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper semicontinuous V-systems. This representation unifies a large class of spatially-variant-linear and nonlinear systems under the same mathematical framework. The theory is used for analyzing special cases of signal and image processing systems such as SV order rank filters and linear-time-varying systems. Finally, simulation results show the potential power of the general theory of gray-level SV mathematical morphology in several image analysis and computer vision applications.
We present a novel formulation that employs task-specific muscle synergies and state-space representation of neural signals to tackle the challenging myoelectric control problem for lower arm prostheses. The proposed framework incorporates information about muscle configurations, e.g., muscles acting synergistically or in agonist/antagonist pairs, using the hypothesis of muscle synergies. The synergy activation coefficients are modeled as the latent system state and are estimated using a constrained Kalman filter. These task-dependent synergy activation coefficients are estimated in real-time from the electromyogram (EMG) data and are used to discriminate between various tasks. The task discrimination is helped by a post-processing algorithm that uses posterior probabilities. The proposed algorithm is robust as well as computationally efficient, yielding a decision with > 90% discrimination accuracy in approximately 3 ms . The real-time performance and controllability of the algorithm were evaluated using the targeted achievement control (TAC) test. The proposed algorithm outperformed common machine learning algorithms for single- as well as multi-degree-of-freedom (DOF) tasks in both off-line discrimination accuracy and real-time controllability (p < 0.01).
Abstract-In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (that is, SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV gray-level morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper semicontinuous V-systems. This representation unifies a large class of spatially-variant-linear and nonlinear systems under the same mathematical framework. The theory is used for analyzing special cases of signal and image processing systems such as SV order rank filters and linear-time-varying systems. Finally, simulation results show the potential power of the general theory of gray-level SV mathematical morphology in several image analysis and computer vision applications.
Magnetic resonance images of brain tumors are routinely used in neuro-oncology clinics for diagnosis, treatment planning, and post-treatment tumor surveillance. Currently, physicians spend considerable time manually delineating different structures of the brain. Spatial and structural variations, as well as intensity inhomogeneity across images, make the problem of computer-assisted segmentation very challenging. We propose a new image segmentation framework for tumor delineation that benefits from two state-of-the-art machine learning architectures in computer vision, i.e., Inception modules and U-Net image segmentation architecture. Furthermore, our framework includes two learning regimes, i.e., learning to segment intra-tumoral structures (necrotic and non-enhancing tumor core, peritumoral edema, and enhancing tumor) or learning to segment glioma sub-regions (whole tumor, tumor core, and enhancing tumor). These learning regimes are incorporated into a newly proposed loss function which is based on the Dice similarity coefficient (DSC). In our experiments, we quantified the impact of introducing the Inception modules in the U-Net architecture, as well as, changing the objective function for the learning algorithm from segmenting the intra-tumoral structures to glioma sub-regions. We found that incorporating Inception modules significantly improved the segmentation performance ( p < 0.001) for all glioma sub-regions. Moreover, in architectures with Inception modules, the models trained with the learning objective of segmenting the intra-tumoral structures outperformed the models trained with the objective of segmenting the glioma sub-regions for the whole tumor ( p < 0.001). The improved performance is linked to multiscale features extracted by newly introduced Inception module and the modified loss function based on the DSC.
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