Unified Mathematical Formulation of Monogenic Phase Congruency

Phase congruency is a technique that has been used for edge, corner and symmetry detection. Its implementation through the use of monogenic filters has improved its computational cost. For this purpose, different methods of implementation have been published, but they do not use a common notation, which makes it difficult to understand. Therefore, this paper presents a unified mathematical formulation that allows a general understanding of the Monogenic phase congruency concepts and establishes criteria for its use. A new protocol for parameter tuning is also described, allowing better practical results to be obtained with this technique. Some examples are presented allowing one to observe the changes produced in the parameter tuning, evidencing the validity of the proposed criteria.

Symmetry Detection and Analysis of Chinese Paifang Using 3D Point Clouds

The Chinese paifang is an essential constituent element for Chinese or many other oriental architectures. In this paper, a new method for detection and analysis of the reflection symmetry of the paifang based on 3D point clouds is proposed. The method invokes a new model to simultaneously fit two vertical planes of symmetry to the 3D point cloud of a paifang to support further symmetry analysis. Several simulated datasets were used to verify the proposed method. The results indicated that the proposed method was able to quantity the symmetry of a paifang in terms of the RMSE obtained from the ICP algorithm, with resistance to the presence of some random noise added to the simulated measurements. For real datasets, three old Chinese paifangs (with ages from 90 to 500 years) were scanned as point clouds to input into the proposed method. The method quantified the degree of symmetry for the three Chinese paifangs in terms of the RMSE, which ranged from 20 to 61 mm. One of the paifangs with apparent asymmetry had the highest RMSE (61 mm). Other than the quantification of the symmetry of the paifangs, the proposed method could also locate which portion of the paifang was relatively more symmetric. The proposed method can potentially be used for structural health inspection and cultural studies of the Chinese paifangs and some other similar architecture.

Optinalysis: A New Method of Data Analysis and Comparison

The key concepts in symmetry detection and similarity, identity measures are automorphism and isomorphism respectively. Therefore, methods for symmetry detection and similarity, identity measures should be functionally bijective, inverse, and invariance under a set of mathematical operations. Nevertheless, few or no existing method is functional for these properties. In this paper, a new methodological paradigm, called optinalysis, is presented for symmetry detections, similarity, and identity measures between isoreflective or autoreflective pair of mathematical structures. The paradigm of optinalysis is the re-mapping of isoreflective or autoreflective pairs with an optical scale. Optinalysis is characterized as invariant under a set of transformations and its isoreflective polymorphism behaves on polynomial and non-polynomial models.

LSM-SEC: Tongue Segmentation by the Level Set Model with Symmetry and Edge Constraints

Accurate segmentation of the tongue body is an important prerequisite for computer-aided tongue diagnosis. In general, the size and shape of the tongue are very different, the color of the tongue is similar to the surrounding tissue, the edge of the tongue is fuzzy, and some of the tongue is interfered by pathological details. The existing segmentation methods are often not ideal for tongue image processing. To solve these problems, this paper proposes a symmetry and edge-constrained level set model combined with the geometric features of the tongue for tongue segmentation. Based on the symmetry geometry of the tongue, a novel level set initialization method is proposed to improve the accuracy of subsequent model evolution. In order to increase the evolution force of the energy function, symmetry detection constraints are added to the evolution model. Combined with the latest convolution neural network, the edge probability input of the tongue image is obtained to guide the evolution of the edge stop function, so as to achieve accurate and automatic tongue segmentation. The experimental results show that the input tongue image is not subject to the external capturing facility or environment, and it is suitable for tongue segmentation under most realistic conditions. Qualitative and quantitative comparisons show that the proposed method is superior to the other methods in terms of robustness and accuracy.