The support vector machine (SVM) combined with the K-nearest neighbor (KNN) algorithm is applied to the 3D image recognition algorithm to cope with the issues of 3D image recognition in the image processing process. In this paper, the KNN algorithm is used to extend the eigenvalues of the residual network from frequency to complex plane according to the eigenvalues of 3D images, and the relevant data are extracted from the images by using the corresponding separation rules of the SVM. Subsequently, a sparse observation model is established based on the SVM combined with the KNN, and the 3D image processing issue is converted to a residual network visualization issue of 3D image recognition by establishing a parameterized database. Meanwhile, detection of high-resolution distance of 3D images is conducted, and the variational inference method is used to visualize and analyze the 3D images accordingly. Finally, through the experimental study, it can be known that the method of SVM combined with the KNN algorithm can reach an accuracy of up to 94.18% in the dataset of the Princeton 3D polygonal models. After comparison with the existing SVM-KNN method and deep learning, it can be concluded that the method put forward in this paper has a higher recognition rate and stronger anti-interference capacity, and the algorithm has a superior convergence speed with less adjustment parameters.