A Study on Geometrical Consistency of Surfaces Using Partition-Based PCA and Wavelet Transform in Classification

The proposed study explores the consistency of the geometrical character of surfaces under scaling, rotation and translation. In addition to its mathematical significance, it also exhibits advantages over image processing and economic applications. In this paper, the authors used partition-based principal component analysis similar to two-dimensional Sub-Image Principal Component Analysis (SIMPCA), along with a suitably modified atypical wavelet transform in the classification of 2D images. The proposed framework is further extended to three-dimensional objects using machine learning classifiers. To strengthen fairness, we benchmarked against both Random Forest (RF) and Support Vector Machine (SVM) classifiers using nested cross-validation, showing consistent gains when TIFV is included. In addition, we carried out a robustness analysis by introducing Gaussian noise to the intensity channel, confirming that TIFV degrades much more gracefully compared to traditional descriptors. Experimental results demonstrate that the method achieves improved performance compared to traditional hand-crafted descriptors such as measured values and histogram of oriented gradients. In addition, it is found to be useful that this proposed algorithm is capable of establishing consistency locally, which is never possible without partition. However, a reasonable amount of computational complexity is reduced. We note that comparisons with deep learning baselines are beyond the scope of this study, and our contribution is positioned within the domain of interpretable, affine-invariant descriptors that enhance classical machine learning pipelines.