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Aircraft Reconstruction in High Resolution SAR Images Using Deep Shape Prior
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摘要: 目标重建是合成孔径雷达图像分析中的重要研究内容。该文提出了一种新的基于深度形状先验的高分辨率合成孔径雷达图像飞机目标重建方法。该方法分为两个阶段，在形状先验建模阶段，利用产生式的深度玻尔兹曼机模型进行深度形状先验建模；在目标重建阶段，提出了一种新的目标重建框架，该框架将深度形状先验作为约束融入重建过程中。为了解决目标旋转问题，该文提出了一种新的姿态估计方法获取目标的候选姿态，避免了姿态的穷举搜索。除此之外，该文构造了融合散射区域项和形状先验项的能量函数，并利用迭代优化算法进行函数优化，从而获取目标重建结果。该文提出的方法框架是首次利用深度形状先验在高分辨率合成孔径雷达图像中实现复杂目标的重建。在TerraSAR-X数据集上的实验结果表明，该文提出的方法具有较高的重建精度和鲁棒性。Abstract: Object reconstruction is of vital importance in Synthetic Aperture Radar (SAR) image analysis. In this paper, we propose a novel method based on shape prior to reconstruct aircraft in high resolution SAR images. The method mainly contains two stages. In the shape prior modeling stage, a generative deep learning method is used to model deep shape priors; a novel framework is then proposed in the reconstruction stage, which integrates the shape priors in the process of reconstruction. Specifically, to address the issue of object rotation, a novel pose estimation method is proposed to obtain candidate poses, which avoids making an exhaustive search for each pose. In addition, an energy function combining a scattering region term and a shape prior term is proposed; this is optimized via an iterative optimization algorithm to achieve the goal of object reconstruction. To the best of our knowledge, this is the first attempt made to reconstruct objects with complex shapes in SAR images using deep shape priors. Experiments are conducted on the dataset acquired by TerraSAR-X and results demonstrate the accuracy and robustness of the proposed method.
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图 2 8种特定角度下10种不同种类的飞机目标黑白二值模板(从上到下角度依次是0°, 315°, 270°, 225°, 180°, 135°, 90°和45°)
Figure 2. Original black and white binary templates of ten types of aircrafts in 8 different poses (Poses, from top to bottom, are 0°, 315°, 270°, 225°, 180°, 135°, 90° and 45°)
图 3 形状对齐结果(第1行和第2行分别表示0°姿态下原始形状模板和形状对齐后的结果图像)
Figure 3. Results of shape alignment (The first and second rows represent the original templates and the results of shape alignment respectively)
图 7 不同目标重建方法的结果对比(第1行与第2行分别对应提取目标区域的轮廓图和提取到的目标区域图)
Figure 7. Comparison of reconstruction results of different methods (The first and the second rows correspond to the contour of the extracted aircraft area and the extracted aircraft area)
表 1 算法1：目标重建中的优化算法
Table 1. The optimization algorithm in object reconstruction
输入：通过预训练和候选姿态选择得到的深度形状先验参数，融合变换因子 ${\rm{\{ }}{{W}^1},{{W}^2},{{a}^1},{{a}^2},{b}{\rm{\} }}$，姿态估计的输出图像u
步骤1 初始化：q为形状模板均值， ${{h}^{\bf{2}}}{\bf{ = 0}}$, ${η} = \left\{ {0.2{\rm{e}} - 5,\;} \right.$ $\left. {3{\rm{e}} - 5,\;3{\rm{e}} - 5,\;0.01{\rm{e}} - 5} \right\}$, $φ = \left\{ {{x_0},{y_0},{h_{{\rm{init}}}},0} \right\}$, ${E^{\rm new}} = 0$, $\tau = 0.1$, ${{I}_1}$, ${{I}_2}$。
步骤2 优化：重复(a)到(c)直到 $|{E^{\rm new}} - E_1^{\rm old}| < \varepsilon $或者达到最大迭代次数 ${{I}_1}$：
(a) 计算 ${W}_φ^1$，并令 $E_1^{\rm old} = {E^{\rm ew}}$；
(b) 重复(i)到(v)直到 $|{E^{\rm new}} - E_1^{\rm old}| < \varepsilon $或者达到最大迭代次数 ${{I}_2}$：
(i) $E_2^{\rm old} = {E^{\rm new}}$，
(ii) ${h^1} = \sigma {\rm{ }}{\left( {{q^{\rm{T}}}W_\varphi ^1 + {W^2}{h^2} + {a^1}} \right)^{\rm{T}}}$，
(iii) $q = \arg \min |\nabla q{|_{\rm{e}}} + \alpha {q^{\rm{T}}}s - \beta ({q^{\rm{T}}}W_\varphi ^1{h^1} + {q^{\rm{T}}}b)$，
(iv) ${h^2} = \sigma \left( {{h^{{1^{\rm{T}}}}}{W^2} + {a^2}} \right)$，
(v) 根据式(4)计算 ${E^{\rm new}}$；
(c) 梯度下降法更新 $φ $：
(i) 利用下面公式计算 $\nabla φ = \left\{ {\nabla x,\nabla y,\nabla h,\nabla \theta } \right\}$：
$\begin{array}{l}\nabla x = \beta {{q}^{\rm T}}{{W}_{x}}{{h}^{{1^{\rm T}}}},\nabla y = \beta {{q}^{\rm T}}{{W}_{\!\! {y}}}{{h}^{{1^{\rm T}}}}\\\nabla h{{ = }}{W}_{x}^{\rm T}({x}{π} \cos \theta - {y}\sin \theta ) + {W}_{y}^{\rm T}({x}\sin \theta + {y}\cos \theta )\\\nabla \theta {{ = }}h\left\{ {{W}_{x}^{\rm T}( - {x}\sin \theta {\rm{ - }}{y}\cos \theta ) + {W}_{y}^{\rm T}({x}\cos \theta - {y}\sin \theta )} \right\}\end{array}$
$({\rm ii}) \ {\text {计算}}φ = φ - {η} \nabla φ {\text{。}}$
输出：最新的形状q。
下载: 导出CSV
表 2 算法：算法1步骤2(b)(iii)算法
Table 2. The algorithm for step 2(b)(iii) in Tab. 1
输入：各变量值
步骤1 初始化：设置参数 $\alpha $, $\beta $。
步骤2 重复步骤(a)到(e)直到 $\parallel{{q}^{k + 1}} - {{q}^k}{\parallel^2} < \varepsilon $
(a) 计算 ${{z}^k} = {(c_1^k - {u})^2} - {(c_2^k - {u})^2} - \beta ({W}_{\! φ}^{{1}}{{h}^{{1}}}{\bf{ + }}{b})$
(b) 最优化 $({{q}^{k + 1}},{\overrightarrow {d} ^{k + 1}}) = \arg \min |\overrightarrow {d} {|_{\rm{e}}} + \alpha {{q}^{\rm T}}{{z}^k} + \frac{\lambda }{2}\parallel\overrightarrow {d} - \nabla {q} - {\overrightarrow {e} ^k}{\parallel^2}$
(i) 最优化 ${{q}^{k + 1}} = \arg \min \alpha {{q}^{\rm T}}{{z}^k} + \frac{\lambda }{2}\parallel{\overrightarrow {d} ^k} - \nabla {q} - {\overrightarrow {e} ^k}{\parallel^2}$, ${{q}^{k + 1}} = {\rm GS}({{z}^k},{\overrightarrow {d} ^k},{\overrightarrow {e} ^k})$
(ii) 最优化 ${\overrightarrow {d} ^{k + 1}} = \arg \min |\overrightarrow {d} | + \frac{\lambda }{2}\parallel\overrightarrow {d} - \nabla {{q}^{k + 1}} - {\overrightarrow {e} ^k}{\parallel^2}$ ${\overrightarrow {d} ^{k + 1}} = {\rm shrin}{{\rm k}_g}({\overrightarrow {e} ^k} + \nabla {{q}^{k + 1}},\lambda )$
(c) 计算 ${\overrightarrow {e} ^{k + 1}} = {\overrightarrow {e} ^k} + \nabla {{q}^{k + 1}} - {\overrightarrow {d} ^{k + 1}}$
(d) 计算 ${Ω}_{τ} ^{ k} = \{ {x}:{{q}^{k + 1}}({x}) > \tau \} $
(e) 更新 $c_1^{k + 1} = \int_{{Ω} _\tau ^{\!\! k}} {{u}{\mathop{\rm d}\nolimits} {x}}, \ c_2^{k + 1} = \int_{{Ω} /{Ω}_\tau ^{\! k}} {{u}{\mathop{\rm d}\nolimits} {x}} $
输出：最新的q。
下载: 导出CSV
表 3 不同目标重建方法的性能比较
Table 3. Performance of different reconstruction methods
方法 平均像素误分比(%) GraphCut方法 40.3 SG-ACM 14.6 去除形状项的本文方法 31.8 本文方法 8.0
下载: 导出CSV
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