A New Multiscale Representation for Shapes and Its Application to Blood Vessel Recovery

In this paper, we will first introduce a novel multiscale representation (MSR) for shapes. Based on the MSR, we will then design a surface inpainting algorithm to recover 3D geometry of blood vessels. Because of the nature of irregular morphology in vessels and organs, both phantom and real inpainting scenarios were tested using our new algorithm. Successful vessel recoveries are demonstrated with numerical estimation of the degree of arteriosclerosis and vessel occlusion.Comment: 12 pages, 3 figure

Combined forecast model involving wavelet-group methods of data handling for drought forecasting

Vigorous efforts to improve the effectiveness of drought forecasting models has yet to yield accurate result. The situation gives room on the use of robust forecasting methods that could effectively improve existing methods. The complex nature of time series data does not enable one single method that is suitable in all situations. Thus, a combined model that will provide a better result is then proposed. This study introduces a wavelet and group methods of data handling (GMDH) by integrating discrete wavelet transform (DWT) and GMDH with transfer functions such as sigmoid and radial basis function (RBF) to form three wavelet-GMDH models known as modified W-GMDH (MW-GMDH), sigmoid W-GMDH (SW-GMDH) and RBF W-GMDH. To assess the effectiveness of this approach, these models were applied to rainfall data at four study stations namely Arau and Kuala Krai in Malaysia as well as Badeggi and Duku-Lade in Nigeria. These data were transformed into four Standardized Precipitation Index (SPI) known as SPI3, SPI6, SPI9 and SPI12. The result shows that the integration of DWT improved the performance of the conventional GMDH model. The combination of these models further improved the performance of each model. The proposed model provides efficient, simple, and reliable accuracy when compared with other models. The incorporation of wavelet to the study results in improving performance for all four stations with the Combined W-GMDH (CW-GMDH) and Combined Regression W-GMDH (CRW-GMDH) models. The results show that Duku-Lade station produced the lowest value of 0.0239 and 0.0211 for RMSE and MAE and highest value of 0.9858 for R respectively. In addition, CRW-GMDH model produce the lowest value of 0.0168 and 0.0117, and the highest value of 0.9870 for RMSE MAE, and R respectively. On the percentage improvement, Duku-Lade station shows improvement over other models with the reductions in RMSE and MAE by 42.3% and 80.3% respectively. This indicates that the model is most suitable for the drought forecasting in this station. The results of the comparison among the four stations indicate that the CW-GMDH and CRW-GMDH models are more accurate and perform better than MW-GMDH, SW-GMDH and RBFW-GMDH models. However, the overall performance of the CRW-GMDH model outweigh that of the CW-GMDH model. In conclusion, CRW-GMDH model performs better than other models for drought forecasting and capable of providing a promising alternative to drought forecasting technique