目的 模糊图像的分析与识别是图像分析与识别领域的重要方向。有些图像形成过程中成像系统与物体之间存在相对旋转运动，如因导弹高速自旋转造成的制导图像的旋转运动模糊。大多数对于这类图像的识别都需要先对模糊图像进行“去模糊”的预处理，且该类方法存在计算时间复杂度较高及不适定的问题。对此，提出一种直接提取旋转运动模糊图像中的不变特征，用于旋转运动模糊图像目标检索和识别。方法 本文以旋转运动模糊的退化模型为出发点，提出了旋转运动模糊Gaussian-Hermite (GH)矩，构造了一组由5个对旋转变换和旋转运动模糊保持不变性的GH矩不变量组成的特征向量(rotational motion blur Gaussian-Hermite moment invariants，RMB_GHMI-5)，可从旋转变换和旋转运动模糊的图像中直接进行目标检索和识别，无需前置复杂的“去模糊”预处理过程。结果 在USC-SIPI (University of Southern California — Signal and Image Processing Institute)数据集上进行不变性实验，对原图进行不同程度的旋转变换叠加旋转运动模糊处理，证明RMB_GHMI-5对于旋转变换和旋转运动模糊具有良好的稳定性和不变性。在两个数据集上与同类4种方法进行图像检索实验比较，在80%召回率下，本文方法维数更少，相比性能第2的特征向量，在Flavia数据集中，高斯噪声、椒盐噪声、泊松噪声和乘性噪声干扰下的准确率分别提高25.89%、39.95%、22.79%和35.80%；在Butterfly Image数据集中，高斯噪声、椒盐噪声、泊松噪声和乘性噪声干扰下的准确率分别提高4.79、7.63%、5.65%和18.31%。同时，在上述8个测试数据集中进行对比实验以验证融合算法的有效性，结果表明本文提出的GH矩和几何矩相融合算法显著改善了图像检索效果。结论 本文提出的RMB_GHMI-5特征向量在旋转变换和旋转运动模糊下具有良好的不变性与稳定性，在图像检索抗噪性能方面表现优异。相比同类方法，本文方法更具实际应用价值。

Objective The blurred image based target recognition issue is essential to computer vision and pattern recognition. In the process of camera imaging exposure, Image degradation is affected by varied environmental and practical factors like atmospheric interference, camera defocus, relative motion between camera and scene. Therefore, the ideal image features should be invariant to these changes. Image motion blur is caused by and relative motion between camera and scene in the process of exposure time. It can be regarded as the integral of image density function in a certain time interval. According to the motion form of the camera relative to the scene in the three-dimensional space in the exposure time, the motion blur of the image can be divided into linear motion blur, rotational motion blur, radial motion blur and other more complex motion blur formed by the superposition of the above three kinds of blurs. In particular, captured images of high-speed rotating status will produce rotational motion blur. In the aspect of pattern recognition of motion blurred image, most of the works choose the strategy of "deblurring". They carry on the next level image processing after restoring the blurred image as clear as possible. If the preprocessing process of image restoration is eliminated and the image features with motion blur invariance are extracted directly, the efficiency of image recognition will be accelerated. Therefore, recent invariant features constructed motion blurred images has become an important research direction in the field of image recognition. Our research method is focused on sort the invariant features out between original image and blurred image through the mathematical model of blurring and the theory of moment invariants. Method When there is relative motion between the object and the photosensitive element, distorted accumulation of light on the imaging plane will occur in one shutter time, resulting in motion blurred image. The blur path can be regarded as a series of concentric circles centered on the camera and the object in terms of axial rotation between the sensor and the object. The rotational motion of variable speed can be decomposed into standardized multiple rotational motions due to the extremely glimpsed shutter time. We will focus on the rotational motion blur standardization related to known rotation center and constant angular velocity based on degraded model of rotation motion blur and Gaussian-Hermite moment. Our method demonstrated the rotational motion blur Gaussian-Hermite moment built issues and facilitated the existing of low-rank rotational motion blur Gaussian-Hermite moment invariants. Correspondingly, the formation of this kind of image is the superposition mean value of the results of a series of rotation transformations on the original image based on the rotation motion blur degradation model. We illustrated that the rotational motion blur Gaussian-Hermite moments is a linear combination of the Gaussian-Hermite moments of the original image. The construction process of rotational motion blur invariants is the process of eliminating the coefficients of Gaussian-Hermite moments of the original image based on Gaussian-Hermite moments. In this way, Gaussian-Hermite moment based rotational motion blur invariants on is built. We filtrated 5 Gaussian-Hermite moment invariants from exiting rotational geometry moment invariants which had been extended to Gaussian-Hermite moment invariants to construct a highly stable 5-dimensional feature vector and named it as rotational motion blur Gaussian-Hermite moment invariants(RMB_GHMI-5), and we verified that RMB_GHMI-5 had great properties of invariability and distinguishability. Finally, we introduced RMB_GHMI-5 to the field of image retrieval. Result In invariance experiment, we validated the invariance ability of the feature vector on the dataset University of Southern California-Signal and Image Processing Institute(USC-SIPI). Two sets of 18 composited blurred images have been made to test RMB_GHMI-5. Our results demonstrate that the feature distance between original image and composited blurred image are extremely weak, which means RMB_GHMI-5 has great invariant attributes. In addition to the image retrieval experiments, we introduce two image datasets in the context of Flavia and Butterfly for original image. Such composited images are blurred of different degree of rotation, rotational motion and Gaussian noise or salt-pepper noise has been used to validate the invariability and distinguishability of RMB_GHMI-5. Compared to 4 distinctive saliency approaches related to leaf images, rotated degrading, rotational motion and Gaussian noise at 80% recall rate, the recognition accuracy of RMB_GHMI-5 is 25.89% higher than salt-pepper noise (39.95%), Poisson noise (22.79%) and multiplicative noise (35.80%). For Butterfly Images degraded by rotation, rotational motion and Gaussian noise at 80% recall rate, the recognition accuracy of RMB_GHMI-5 is 7.18% higher than salt-pepper noise (39.95%), Poisson noise (22.79%) and multiplicative noise (35.80%). Conclusion We proposed a 5-dimensional feature vector RMB_GHMI-5 which is invariable for rotational motion blur based on Gaussian-Hermite moments. We verified that RMB_GHMI-5 had great potentials of invariability and distinguishability in the field of image retrieval. Our experimental results demonstrate that RMB_GHMI-5 has its priority related to current saliency approaches.