Artifact removal and texture-based rendering for visualization of 3D fetal ultrasound images

Abstract

Convenient and non-invasive ultrasonography has become an essential tool for diagnosing fetal abnormalities. However, the noisy and blurry nature of sonographic data poses a challenge. To improve object visualization, we first develop a modified diffusion filter that utilizes the local standard deviation and edge of local-average-difference to define an adaptive edge stopping function in diffusion filtering. The proposed method overcomes the drawbacks of traditional diffusion filters and shows good results in comparative experiments. Moreover, we propose a novel light absorbing function to remove large regions of interface artifacts. An advanced imaging mode, called texture-based rendering, is employed to provide more realistic rendering. Experimental results show that the proposed methods enhance final image quality in 3D fetal sonograms.

Appendix

The following is the derivation of the normal vector.

$$\overrightarrow{N}= \frac{1}{8} \cdot \left({\sum_{i = 1}^4 \overrightarrow{P_{s}N_{i}} \times\overrightarrow{P_{s}N_{{\rm mod}(i+1)}}} + {\sum_{i = 5}^8 \overrightarrow{P_{s}N_{i}} \times\overrightarrow{P_{s}N_{{\rm mod}(i+1)}}}\right) $$

(A1)

Substituting the coordinates of P _s and N _i into (A1) yields

$$ \begin{aligned}\mathop{N}\limits^{\rightharpoonup} &= \frac{1}{8} \cdot ((0, - 1,D_{1} - D_{s}) \times (- 1,0,D_{2} - D_{s}) + (- 1,0,D_{2} - D_{s}) \times (0,1,D_{3} - D_{s}) \\&\quad + (0,1,D_{3} - D_{s}) \times (1,0,D_{4} - D_{s}) + (1,0,D_{4} - D_{s}) \times (0, - 1,D_{1} - D_{s}) \\&\quad + (1, - 1,D_{5} - D_{s}) \times (- 1, - 1,D_{6} - D_{s}) + (- 1, - 1,D_{6} - D_{s}) \times (- 1,1,D_{7} - D_{s}) \\&\quad + (- 1,1,D_{7} - D_{s}) \times (1,1,D_{8} - D_{s}) + (1,1,D_{8} - D_{s}) \times (1, - 1,D_{5} - D_{s})) \\\end{aligned}. $$

(A2)

where × denotes the cross product operation. To simplify the equation, we define ∇ D _i as D _i −D _s so that

$$ \begin{aligned}\mathop{N}\limits^{\rightharpoonup}& = \frac{1}{8} \cdot ((0, - 1,\nabla D_{1}) \times (- 1,0,\nabla D_{2}) + (- 1,0,\nabla D_{2}) \times (0,1,\nabla D_{3}) \\&\quad + (0,1,\nabla D_{3}) \times (1,0,\nabla D_{4}) + (1,0,\nabla D_{4}) \times (0, - 1,\nabla D_{1}) \\&\quad + (1, - 1,\nabla D_{5}) \times (- 1, - 1,\nabla D_{6}) + (- 1, - 1,\nabla D_{6}) \times (- 1,1,\nabla D_{7}) \\&\quad + (- 1,1,\nabla D_{7}) \times (1,1,\nabla D_{8}) + (1,1,\nabla D_{8}) \times (1, - 1,\nabla D_{5})). \\\end{aligned} $$

(A3)

After expanding the cross product, (A3) becomes

$$ \begin{aligned}\mathop{N}\limits^{\rightharpoonup}& = \frac{1}{8} \cdot ((- \nabla D_{2}, - \nabla D_{1}, - 1) + (- \nabla D_{2}, \nabla D_{3}, - 1) + (\nabla D_{4}, \nabla D_{3}, - 1) + (\nabla D_{4}, - \nabla D_{1}, - 1) \\&\quad + (\nabla D_{5} - \nabla D_{6}, - \nabla D_{5} - \nabla D_{6}, - 2) + (- \nabla D_{6} - \nabla D_{7}, \nabla D_{7} - \nabla D_{6}, - 2) \\&\quad + (\nabla D_{8} - \nabla D_{7}, \nabla D_{7} + \nabla D_{8}, - 2) + (\nabla D_{5} + \nabla D_{8}, \nabla D_{8} - \nabla D_{5}, - 2)) \\\end{aligned} $$

(A4)

$$ \Rightarrow \mathop{N}\limits^{\rightharpoonup}= \frac{1}{8} \cdot {\left[ \begin{aligned}& 2 \cdot {\left({\nabla D_{4} - \nabla D_{2} + \nabla D_{5} - \nabla D_{7} + \nabla D_{8} - \nabla D_{6}} \right)} \\& 2 \cdot {\left({\nabla D_{3} - \nabla D_{1} + \nabla D_{7} - \nabla D_{5} + \nabla D_{8} - \nabla D_{6}} \right)} \\& - 12 \\\end{aligned} \right]} $$

(A5)

$$ \Rightarrow \mathop{N}\limits^{\rightharpoonup}= {\left[ \begin{aligned}& \frac{1}{4} \cdot {\left({\nabla D_{4} - \nabla D_{2} + \nabla D_{5} - \nabla D_{7} + \nabla D_{8} - \nabla D_{6}} \right)} \\& \frac{1}{4} \cdot {\left({\nabla D_{3} - \nabla D_{1} + \nabla D_{7} - \nabla D_{5} + \nabla D_{8} - \nabla D_{6}} \right)} \\& - \frac{3}{2} \\\end{aligned} \right]} $$

(A6)