The objects’ features play significant role in the machine learning (ML) classification. The present paper proofs and validates that the shapes of vector field (VF) singular points (SPs) embedded into image objects may improve classification accuracy. For this purpose the present paper develops two VFs vû and v ˆ ϕ with real and complex SPs. The VFs are developed on the solution û(x, y) of a particular form of the Poisson equation. Further, we define the mappings between the SPs of ∇û(x, y), vû and v ˆ ϕ. Next, we develop the local Polya’s model of a VF and prove that the shapes of the SPs are invariant according to scaling, translation and weak rotations. This property implies that embedding the shapes of the SPs into the image objects extends the set of objects features, which leads to the advantage of increasing the classification statistics. We validate the invariance and the advantage with sets of experiments classifying the public image datasets ISIC2020 and COIL100. For the purpose of classification, we designed a new convolution neural network optimized to classify SP shapes and image objects features. The paper ends with conclusions on the contributions, advantages and the bottlenecks of this study.