In the article, we proposed a hybridized method for brain tumor image segmentation by fusing topological heterogeneities of images and the attention mechanism in the neural networks. The three-dimensional image datasets were first pre-processed using the histogram normalization for the standardization of pixel intensities. Then the normalized images were parallel fed into the procedures of affine transformations and feature pre-extractions. The technique of fast data density functional theory (fDDFT) was adopted for the topological feature extractions. Under the framework of fDDFT, 3-dimensional topological features were extracted and then used for the 2-dimensional tumor image segmentation, then those 2-dimensional significant images are reconstructed back to the 3-dimensional intensity feature maps by utilizing physical perceptrons. The undesired image components would be filtered out in this procedure. Thus, at the pre-processing stage, the proposed framework provided dimension-hybridized intensity feature maps and image sets after the affine transformations simultaneously. Then the feature maps and the transformed images were concatenated and then became the inputs of the attention U-Net. By employing the concept of gate controlling of the data flow, the encoder can perform as a masked feature tracker to concatenate the features produced from the decoder. Under the proposed algorithmic scheme, we constructed a fast method of dimension-hybridized feature pre-extraction for the training procedure in the neural network. Thus, the model size as well as the computational complexity might be reduced safely by applying the proposed algorithm.