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Visualization provides an interactive investigation of details of interest and improves understanding the implicit information. There is a strong need today for the acquisition of high quality visualization result for various fields, such as biomedical or other scientific field. Quality of biomedical volume data is often impacted by partial effect, noisy, and bias seriously due to the CT (Computed Tomography) or MRI (Magnetic Resonance Imaging) devices, which may give rise to an extremely difficult task of specifying transfer function and thus generate poor visualized image. In this paper, firstly a nonlinear neural network based denoising in the preprocessing stage is provided to improve the quality of 3D volume data. Based on the improved data, a novel region space with depth based 2D histogram construction method is then proposed to identify boundaries between materials, which is helpful for designing the proper semiautomated transfer function. Finally, the volume rendering pipeline with ray-casting algorithm is implemented to visualize several biomedical datasets. The noise in the volume data is suppressed effectively and the boundary between materials can be differentiated clearly by the transfer function designed via the modified 2D histogram.

Since there are the two characteristics of visibility of object and clear detail revealing, visualization has been proven to be of paramount important for exploring meaningful properties of volume data [

Transfer function plays a fundamental role in visualization for its capability of classifying and segmenting features of volume data, which may affect the quality of rendering image and the perception of users to volume data. To measure through-plane MR flow. Thunberg et al. [

Ebert et al. [

Different from the object-centric method, the image centric transfer function is designed on the rendered images. Through the evaluation of the projective images, parameters of transfer function are automatically adjusted and reapplied to the original data recursively until the satisfied rendering result is achieved. Based on a set of rendered images, He et al. [

In data-centric approach, parameters of transfer function are specified by analyzing the volume data. Generally, collecting additional information related to the data prior to confirming transfer function makes the design more convenient. Scalar value of volume data is commonly considered for deriving 1D transfer function. The gradient [

When the dimension is more than 2, it is difficult to specify the parameters for the higher dimensional transfer functions. The histograms are often used to find satisfied transfer functions. Based on the first and second derivatives in the volume, Kindlmann and Durkin [

In this paper, firstly a neural network volume data preprocessing approach for slice denoising is implemented to improve the quality of 3D biomedical data. Then a two-dimensional transfer function with the preprocessed data is designed based on a modified 2D histogram, which is created using a novel region space based method with depth information. The features of interest in the data are thus exactly explored. In Section

Biomedical volume data produced by current noninvasive devices such as CT and MRI scanners are usually accompanied by noisy, partial effect, and bias. Data with serious noise or error message which causes low SNR (Signal Noise Ratio) will directly affect transfer function specification and cause the objects obscuring in the resulting image.

Spatial mean low-pass filtering such as General Median filtering and Gaussian smoothing has the advantage of reducing the amplitude of noise fluctuations. While the filtering blurs the details in the data such as the line or edge and does not focus on processing regional boundary or tiny structures, which makes the resulting image too fuzzy. This is a hamper to effectively enhance boundary for those noisy data containing lots of details.

Although nonlinear filtering has the achievement of reserving the edge, it produces the loss of resolution due to the suppression of details. To solve this problem, the non-linear enhancement algorithm uses information of boundary and the neighbor of a pixel to preprocess the image data [

The architecture of the MLP network.

During application for image denoising, MLP uses fully connected neural network to process image fragments and then splits and combines all processed image segments to form a denoising image. First the noisy image is split into overlapping patches and each patch

Kindlmann et al. [

LH Histogram based method computes low and high values of each sample voxels which are labeled as

In volume rendering, using LH method to design transfer function can not only reduce the dependence on image segmentation, but also include voxel gradient information and boundary gray information. Due to the characteristics of medical data and clinical application, centralization of the voxel is required.

A proper region space

In the region where the complex boundary exists, using the single criterion will result in boundary determination error. Since some boundaries only appear at a certain depth and then disappear when they reach a certain depth, the complex boundaries can be further differentiated according to the depth information. Then a modified 2D histogram is created using the region space based method with depth information. In this paper the points in the original histogram are further grouped according to the corresponding depth.

A 2D transfer function can then be specified based on the created LH histogram by selecting relevant areas and by assigning them color and opacity. The corresponding features in the volume data can thus be explored. The details of the proposed method are given in Algorithm

In this section, some data sets are used as the test data, including tooth data and sheep heart data, to evaluate the performance of the proposed transfer function. The size of data set is 256×256×161 and 352×352×256, respectively. All the experiments are carried out on the computer with Intel Core i5 2.66G, 4.00G RAM and graphics card of NVIDIA GeForce GT 650.

Biomedical volume data produced by current noninvasive devices such as CT and MRI scanners are usually accompanied by serious noise, which will generate poor visualized image and cause the blur objects in the resulting image. Thus the MLP neural network is implemented to denoise the volume data. In the experiments, the union of the LabelMe dataset is used to train MLP which contains approximately 150,000 images. Before training, the data are filled with padding operation and each pixel is filled with 6 pixel sizes. The noise level

Preprocessing results of tooth dataset. From top to bottom: original slice data, denoised images by the nonlinear enhancement algorithm, and denoised images by MLP. (a) Original slice data; (b) nonlinear enhancement denoised result; (c) MLP denoised result.

In LH histogram, points around diagonal represent interior of materials. Regions including those points are thus assigned to lower opacity in the transfer function to fade unimportant information out. Remainder regions are the accumulation of boundary voxels which contain features of interest. Figure

LH histogram and rendering result of the original tooth data and MLP denoised data: (a) LH histogram and the corresponding rendering result of original data and (b) LH histogram and corresponding rendering result of denoised data.

Figure

LH histogram and corresponding rendering result with nonlinear enhanced tooth dataset through the conventional and region criteria based method: (a) LH histogram based on conventional method with gradient threshold of 5 and the corresponding rendering result and (b) LH histogram based on region criteria based method and the rendering result.

Figure

Rendering result of MLP augmented tooth dataset with two methods: (a) rendering result based on region criteria based method and (b) rendering result based on depth enhanced method.

Figure

Visualization result of augmented sheep heart dataset with region space guided transfer function: (a) the original sheep heart data; (b) the denoised data; (c) rendering result of sheep heart with the denoised data.

Transfer function in performance of volume rendering plays a crucial role for exploring directly detail information hiding in data as well as enhancing important boundaries. In this work we first implement the MLP neural network on volume data to denoise while preserve the boundary. This method can considerably improve quality of volume data acquired by devices. Then we improve the LH method by combining the regional depth information to achieve the transfer function semiautomatic generation. This method can avoid the influence of noise and make the voxels more centralized. In the LH histogram the voxel distribution at the diagonal line is more concentrated, and the boundary of important objects are effectively emphasized. The features of interest in the data can thus be found exactly by mapping scalar value of boundary voxels which correspond to the points in LH histogram to appropriate opacity and color.

The two datasets are both open data which are available at

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The work was supported by the National Natural Science Foundation of China (NSFC) under Grant no. 61502275 and the Postdoctoral Science Foundation of China (no. 2017M622210). This work was also supported in part by the Natural Science Foundation of Shandong of Grant no. ZR2017MF051, the National Natural Science Foundation of China (NSFC) of Grant no. 61501450, and the MOE (Ministry of Education in China) Project of Humanities and Social Sciences of Grant no. 16YJC880057.