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WO2019071976A1 - Panoramic image saliency detection method based on regional growth and eye movement model - Google Patents

Panoramic image saliency detection method based on regional growth and eye movement model Download PDF

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WO2019071976A1
WO2019071976A1 PCT/CN2018/091905 CN2018091905W WO2019071976A1 WO 2019071976 A1 WO2019071976 A1 WO 2019071976A1 CN 2018091905 W CN2018091905 W CN 2018091905W WO 2019071976 A1 WO2019071976 A1 WO 2019071976A1
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saliency
panoramic image
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李革
朱春彪
黄侃
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Peking University Shenzhen Graduate School
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  • a look-around monitoring system for an autonomous vehicle uses a panoramic image by combining a plurality of images taken at different viewing positions. These panoramic images can be obtained directly by using a special device, or can be generated by combining several conventional images having small aspect ratios using image stitching techniques.
  • the assumptions for detecting the saliency of a conventional image do not fully reflect the characteristics of the panoramic image. Therefore, it is difficult to implement efficient panoramic image processing in the prior art, and the accuracy and robustness of the saliency detection method of the existing panoramic image need to be improved.
  • the principle of the invention is that the panoramic image has different characteristics compared to conventional images.
  • the width of the panoramic image is much larger than the height, so the background is distributed over the horizontally elongated area.
  • the background of a panoramic image is usually composed of several homogeneous regions, such as the sky, mountains, and ground.
  • a typical panoramic image may include multiple foreground objects having different features and sizes that are arbitrarily distributed throughout the image. For these features, it is difficult to design a global method of directly extracting a plurality of salient regions from the input panoramic image.
  • the present invention finds that the spatial density mode is useful for images with high resolution. Therefore, the present invention firstly uses a spatial density pattern detection method based on a region-grown panoramic image to roughly extract a preliminary object.
  • a panoramic image saliency detection method based on regional growth and eye movement model uses a region growing and eye movement fixed point prediction model (referred to as an eye movement model) to realize automatic protruding object detection of a panoramic image; the following steps are included:
  • the image processing method is applied to image enhancement of the intensity image, and then the region growing algorithm is applied to extract significantly different regions, and the exact shape of the distinct regions can be returned, and only the precise shape is output.
  • Rough rectangular bounding box
  • Threshold selection adaptive threshold processing is selected.
  • the spatial support of the foreground is substantially isolated by taking the sign of the mixed signal X in the transform domain, and then converted back to the spatial domain, ie, by reconstructing the reconstructed image
  • the signature model is defined as IS(X):
  • g is the Gaussian kernel.
  • A(p) represents the number of pixels in the p-th region.
  • the present invention utilizes map statistics to determine the importance of each path (steps 1), 2)); in the final integration phase, combining the results of the two paths, they are summed (MN) after Maxima normalization.
  • the weight of the significance value may be sensitive to the geodesic distance.
  • the present invention employs a solution that can more evenly enhance the area of the protruding object.
  • the input image is segmented into a plurality of superpixels according to a linear spectral clustering method, and the posterior probability of each superpixel is calculated by averaging the posterior probability values Sp of all the pixels therein.
  • the significance value of the qth superpixel is improved by the geodesic distance as in Equation 4:
  • J is the total number of superpixels ;
  • wqj is the weighting value of the geodesic distance between the qth superpixel and the jth superpixel .
  • Equation 6 ⁇ pi is the weight value of the geodesic distance between the pth superpixel and the i th superpixel; ⁇ c is the deviation of d c ; d g (p, j) is between pixels p and j Geodesic distance.
  • the saliency of the panoramic image is detected.
  • the invention provides a method for detecting the saliency of a panoramic image by using a region growing algorithm and an eye movement model. Firstly, a spatial density pattern detecting method based on a region-grown panoramic image is used to roughly extract a preliminary object. The eye-fixed model is embedded in the frame to predict visual attention; and the previously obtained saliency information is merged by maximum normalization to obtain a rough saliency map. Finally, geodesic optimization techniques are used to obtain the final saliency map.
  • the invention can solve the problem that the saliency detection precision and the robustness of the prior method are insufficient, and is not suitable for the panoramic picture, so that the saliency area in the panoramic image is more accurately displayed, and provides for the later target recognition and classification applications. Precise and useful information.
  • a new high-quality panoramic data set (SalPan) is constructed, which has a novel ground truth annotation method, which can eliminate the ambiguity of significant objects.
  • the model proposed by the present invention is also applicable to the saliency detection of a conventional image.
  • the method of the present invention can also help to find the perceptual characteristics of the human visual system for large-scale visual content in a wide field of view.
  • FIG. 1 is a flow chart of a detection method provided by the present invention.
  • FIG. 2 is an input panoramic image, another method detection image, a detection image of the present invention, and an artificially calibrated image to be obtained according to an embodiment of the present invention
  • the first behavior input image; the second to sixth behaviors are the detection result images obtained by other methods; the seventh behavior is the detection result image of the present invention; and the eighth behavior is to manually calibrate the desired image.
  • FIG. 3 is a diagram showing the effect of saliency detection applied to a conventional image according to the present invention.
  • the first behavior inputs a regular image
  • the second behavior is a detection result image of the present invention
  • the third behavior manually calibrates the desired image.
  • the invention provides a method for detecting the saliency of a panoramic image by using a region growing algorithm and an eye movement model. Firstly, a spatial density pattern detecting method based on a region-grown panoramic image is used to roughly extract a preliminary object. The eye-fixed model is embedded in the frame to predict visual attention; and the previously obtained saliency information is merged by maximum normalization to obtain a rough saliency map. Finally, using the geodesic optimization technique to obtain the final saliency map, the experimental comparison is shown in Figure 2.
  • FIG. 1 is a block diagram of a saliency detection method provided by the present invention, which includes four main steps. First, we use the region growing algorithm to automate the selection of significant object regions. Second, use the fixed-eye prediction model to estimate significant points. The previous significance information is then fused using the maximum normalization method. Finally, the final significance test results are obtained by geodesic optimization techniques. The detailed process is described as follows:
  • Step 1 Detection based on regional growth.
  • Threshold Use adaptive thresholding. The experimental results show that the algorithm based on region growth works well in detecting important areas with effective computing power. By estimating the density matrix, we can propose some significant regions that can be enhanced or re-estimated in the next step.
  • Step 2 Eye movement fixed point prediction.
  • Whether a location is significant depends largely on its ability to attract attention. A large amount of recent work on eye fixation predictions has more or less revealed the nature of this problem.
  • the fixed-eye prediction model simulates the mechanisms of the human visual system so that it can predict the probability that a location will attract attention. So in this step, we use eye-fixed models to help us ensure which areas are more attractive.
  • Panoramic images typically have a wide field of view and are therefore computationally more expensive than conventional images. Based on the color contrast algorithm, local information is not suitable as a pre-processing step for panoramic images because these algorithms are time consuming and costly computationally intensive. Therefore, the present invention employs a more efficient method to help us scan images quickly and roughly locate where attention is drawn.
  • the fixed prediction model in the frequency domain is computationally efficient and easy to implement. Therefore, the present invention uses the eye movement prediction model in the frequency domain as the signature model.
  • the signature model roughly isolates the spatial support of the foreground by taking the sign of the mixed signal X in the transform domain, and then converts it back into the spatial domain, ie by reconstructing the reconstructed image Indicates the DCT transform of X.
  • the image signature IS(X) is defined as Equation 1:
  • DCT() is a DCT transform function
  • the saliency map is formed by smoothing the squared reconstructed image defined above, expressed as Equation 2.
  • g is the Gaussian kernel.
  • A(p) represents the number of pixels in the p-th region.
  • Step 3 The maximum value is normalized.
  • Step 4 Geodesic technology optimization.
  • the final step in the proposed method is to use the geodesic distance to optimize the final result.
  • the input image is segmented into a plurality of superpixels according to a linear spectral clustering method, and the posterior probability of each superpixel is calculated by averaging the posterior probability values Sp of all the pixels therein.
  • the jth superpixel if its posterior probability is marked as S(j), the significant value of the qth superpixel is improved by the geodesic distance as in Equation 4:
  • J is the total number of superpixels
  • wqj will be based on the weight of the geodesic distance between the qth superpixel and the jth superpixel.
  • J is the total number of superpixels
  • wqj will be based on the weight of the geodesic distance between the qth superpixel and the jth superpixel.

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Abstract

A panoramic image saliency detection method based on regional growth and an eye movement model. The regional growth and a fixed prediction model are used to realize detection of an automatic salient object of a panoramic image. The method comprises: detecting an original image based on regional growth, and roughly extracting an area with a significant density difference compared with a neighbor area by means of a regional growth algorithm to obtain an area with a large density difference; obtaining a saliency value of a salient region by means of eye movement fixed point prediction; carrying out maximum value normalization and then carrying out summing; and enhancing the salient region more uniformly by using a method for optimizing a geodesic line. According to the method, the problems that an existing method has insufficient saliency detection precision and robustness and is not suitable for the panoramic image can be solved, thus the salient region in the panoramic image is more accurately displayed, and accurate and useful information is provided for the later application of target recognition, classification and the like.

Description

基于区域增长和眼动模型的全景图像显著性检测方法Panoramic image saliency detection method based on regional growth and eye movement model 技术领域Technical field

本发明涉及图像处理、计算机视觉和机器人视觉技术领域,尤其涉及一种利用区域增长算法和眼动模型进行全景图像的显著性检测的方法。The invention relates to the field of image processing, computer vision and robot vision technology, and in particular to a method for performing saliency detection of a panoramic image by using a region growing algorithm and an eye movement model.

背景技术Background technique

人眼的固有和强大的能力是快速捕获场景中最突出的地区,并将其传递到高级视觉皮层。注意力选择降低了视觉分析的复杂性,从而使人类视觉系统在复杂场景中效率相当高。作为预处理程序,许多应用程序受益于显着性分析,例如检测异常模式,分割原始对象,生成对象提案,等等。显著性的概念不仅在早期的视觉建模中被研究,而且在诸如图像压缩,对象识别和跟踪,机器人导航,广告等领域也有着广泛的应用。The inherent and powerful ability of the human eye is to quickly capture the most prominent areas of the scene and pass them to the advanced visual cortex. Attentional attention reduces the complexity of visual analysis, making the human visual system quite efficient in complex scenes. As a preprocessor, many applications benefit from saliency analysis, such as detecting anomalous patterns, splitting primitives, generating object proposals, and more. The concept of salience has not only been studied in early visual modeling, but also in fields such as image compression, object recognition and tracking, robot navigation, advertising, etc.

早期的计算显著性的工作旨在模拟和预测人们对图像的注视。最近该领域已经扩展到包括整个突出区域或对象的细分。Early work on computational saliency was designed to simulate and predict people's gaze on images. Recently the field has expanded to include subdivisions of entire highlighted areas or objects.

大部分工作根据中心环绕对比度的概念,提取与周边地区相比具有显著特征的突出区域。此外,还可以使用前景对象和背景的空间布局的附加现有知识:具有很高的属于背景的可能性,而前景突出对象通常位于图像中心附近。已经成功地采用这些假设来提高具有常规纵横比的常规图像的显着性检测的性能。近来,产生广泛视野的全景图像在各种媒体内容中变得流行,在许多实际应用中引起了广泛的关注。例如,当用于诸如头戴式显示器的可穿戴设备时,虚拟现实内容表现出广泛的视野。用于自主车辆的环视监控系统通过组合在不同观看位置拍摄的多个图像来使用全景图像。这些全景图像可以通过使用特殊装置直接获得,或者可以通过使用图像拼接技术组合几个具有小纵横比的传统图像来生成。然而,用于检测常规图像显著性的假设并不能完全反映全景图像的特征。因此,现有技术难以实现高效的全景图像处理,现有的全景图像的显著性检测方法的精确度、健壮性均有待提高。Most of the work extracts a prominent area with significant features compared to the surrounding area based on the concept of center-surrounded contrast. In addition, additional prior knowledge of the spatial layout of foreground objects and backgrounds can be used: there is a high probability of belonging to the background, while foreground highlighted objects are usually located near the center of the image. These assumptions have been successfully employed to improve the performance of saliency detection of conventional images with conventional aspect ratios. Recently, panoramic images that produce a wide field of view have become popular in various media contents, and have attracted widespread attention in many practical applications. For example, when used in a wearable device such as a head mounted display, the virtual reality content exhibits a wide field of view. A look-around monitoring system for an autonomous vehicle uses a panoramic image by combining a plurality of images taken at different viewing positions. These panoramic images can be obtained directly by using a special device, or can be generated by combining several conventional images having small aspect ratios using image stitching techniques. However, the assumptions for detecting the saliency of a conventional image do not fully reflect the characteristics of the panoramic image. Therefore, it is difficult to implement efficient panoramic image processing in the prior art, and the accuracy and robustness of the saliency detection method of the existing panoramic image need to be improved.

发明内容Summary of the invention

为了克服上述现有技术的不足,本发明提供一种利用区域增长算法和眼动模型进行全景图像的显著性检测的方法,能够解决现有方法的显著性检测精确度、健壮性不够,不适用于全景图片的问题,使全景图像中的显著性区域更精准地显现出来,为后期的目标识别和分类等应用提供精准且有用的信息。In order to overcome the deficiencies of the prior art, the present invention provides a method for detecting the saliency of a panoramic image by using a region growing algorithm and an eye movement model, which can solve the saliency detection accuracy and robustness of the existing method, and is not applicable. The problem of panoramic images makes the saliency area in the panoramic image more accurate, providing accurate and useful information for later target recognition and classification applications.

本发明的原理是:与常规图像相比,全景图像具有不同的特征。首先,全景图像的宽度比高度大得多,因此背景分布在水平伸长的区域上。其次,全景图像的背景通常由几个同质区域组成,如天空,山地和地面。此外,典型的全景图像可以包括具有不同特征和尺寸的多个前景对象,它们任意地分布在图像各处。对于这些特征,难以设计从输入全景图像直接提取多个显著区域的全局方法。本发明发现空间密度模式对于具有高分辨率的图像是有用的。因此,本发明首先采用基于区域生长的全景图像的空间密度模式检测方法来粗略提取初步对象。将眼固定模型嵌入到框架中,以预测视觉注意力,这是符合人类视觉系统的方法。然后,通过最大值归一化将先前得到的显著性信息相融合,得出粗略的显著性图。最后,使用测地线优化技术来获得最终的显著性图。The principle of the invention is that the panoramic image has different characteristics compared to conventional images. First, the width of the panoramic image is much larger than the height, so the background is distributed over the horizontally elongated area. Second, the background of a panoramic image is usually composed of several homogeneous regions, such as the sky, mountains, and ground. Moreover, a typical panoramic image may include multiple foreground objects having different features and sizes that are arbitrarily distributed throughout the image. For these features, it is difficult to design a global method of directly extracting a plurality of salient regions from the input panoramic image. The present invention finds that the spatial density mode is useful for images with high resolution. Therefore, the present invention firstly uses a spatial density pattern detection method based on a region-grown panoramic image to roughly extract a preliminary object. Embedding an eye-fixed model into the frame to predict visual attention is a method consistent with the human visual system. Then, the previously obtained saliency information is fused by maximum normalization to obtain a rough saliency map. Finally, geodesic optimization techniques are used to obtain the final saliency map.

本发明提供的技术方案是:The technical solution provided by the invention is:

基于区域增长和眼动模型的全景图像显著性检测方法,使用区域生长和眼动固定点预测模型(简称为眼动模型),实现全景图像的自动突出物体检测;包括如下步骤:A panoramic image saliency detection method based on regional growth and eye movement model uses a region growing and eye movement fixed point prediction model (referred to as an eye movement model) to realize automatic protruding object detection of a panoramic image; the following steps are included:

1)针对原始图像进行基于区域增长的检测,通过区域增长算法粗略地提取与其邻居相比具有显著不同密度的区域;1) performing region-based growth detection on the original image, and roughly extracting regions having significantly different densities compared to their neighbors by a region growing algorithm;

其中,重大差异的区域可以分为三类:1)过密度的区域,2)密度不足的区域,3)由山脊或沟渠包围的地区。具体包括如下过程:Among them, the areas of significant differences can be divided into three categories: 1) areas with excessive density, 2) areas with insufficient density, and 3) areas surrounded by ridges or ditches. Specifically, the following processes are included:

11)开始时,将原始图像分割成M*N个小区域,并转换成密度矩阵,其中每个单位(i,j)表示第(i,j)个小区域内的对象的计数;原始图像经过密度矩阵的处理,得到强度图像。11) At the beginning, the original image is segmented into M*N small regions and converted into a density matrix, where each unit (i, j) represents the count of objects in the (i, j)th small region; the original image passes The processing of the density matrix yields an intensity image.

12)基于作为强度图像处理的该密度矩阵,应用图像处理方法对强度图像进行图像增强,再应用基于区域增长的算法来提取显著不同的区域,可以返回明显不同区域的精确形状,仅输出精确形状的粗糙的矩形边界框;12) Based on the density matrix as the intensity image processing, the image processing method is applied to image enhancement of the intensity image, and then the region growing algorithm is applied to extract significantly different regions, and the exact shape of the distinct regions can be returned, and only the precise shape is output. Rough rectangular bounding box;

为了简单起见,可将原始彩色图像转换为灰度图像,然后将上述采用对象提案算法提取的精确图像的粗糙矩形边界框应用于灰度图像,所得到的图像可以被看作是密度图。基于区域增长的算法来提取显著不同的区域过程中进行如下处理:For the sake of simplicity, the original color image can be converted to a grayscale image, and then the rough rectangular bounding box of the precise image extracted by the object proposal algorithm described above is applied to the grayscale image, and the resulting image can be regarded as a density map. The process of extracting significantly different regions based on the region growing algorithm performs the following processing:

(a)提高密度图像:应用形态学操作,包括形态学扩张,侵蚀,开放和近距离,以消除像非常小的区域之类的噪声,并且连接彼此靠近的单独的同质区域。(a) Increased density image: Apply morphological operations, including morphological expansion, erosion, openness, and close proximity to eliminate noise such as very small areas and connect separate homogeneous regions that are close together.

(b)排除不同的背景地区:后续步骤采用一些优化方法,例如平均强度值和提取区域的总面积以排除不良结果。(b) Exclude different background areas: Subsequent steps use optimization methods such as average intensity values and total area of the extraction area to exclude undesirable results.

(c)种子选择:在实施过程中,自动种子选择和迭代提供阈值。(c) Seed selection: In the implementation process, automatic seed selection and iteration provide thresholds.

(d)阈值选择:选用自适应阈值处理。(d) Threshold selection: adaptive threshold processing is selected.

2)眼动固定点预测,得到突出区域的显著性值;包括如下步骤:2) Eye movement fixed point prediction, obtain the salient value of the highlighted area; including the following steps:

21)使用眼固定模型(眼动模型、固定预测模型)来分析哪个区域会更加吸引人们的注意力,得到显著性区域;21) Use eye fixation models (eye movement models, fixed prediction models) to analyze which areas are more attractive to people's attention and get significant areas;

22)采用频域中的固定预测模型快速扫描图像,并粗略地定位吸引人们关注的地方;22) Using a fixed prediction model in the frequency domain to quickly scan the image and roughly locate the places that attract people's attention;

23)采用签名模型,通过取变换域中的混合信号X的符号大致隔离前景的空间支持,然后将其转换回空间域,即通过计算重构图像

Figure PCTCN2018091905-appb-000001
表示X的DCT变换;签名模型被定义为IS(X): 23) Using the signature model, the spatial support of the foreground is substantially isolated by taking the sign of the mixed signal X in the transform domain, and then converted back to the spatial domain, ie, by reconstructing the reconstructed image
Figure PCTCN2018091905-appb-000001
A DCT transform representing X; the signature model is defined as IS(X):

IS(X)=sign(DCT(X))                 (式1)IS(X)=sign(DCT(X)) (Formula 1)

通过平滑上面定义的平方重建图像形成显著性图,表示为式2:A saliency map is formed by smoothing the squared reconstructed image defined above, expressed as Equation 2:

Figure PCTCN2018091905-appb-000002
Figure PCTCN2018091905-appb-000002

其中,g表示高斯内核。Where g is the Gaussian kernel.

24)将提取出的突出区域与图像签名产生的显著性图像S m进行组合,通过对其中所有像素的显著性进行平均值来分配所提取出的突出区域的显著性值; 24) combining the extracted protruding area with the saliency image S m generated by the image signature, and assigning the saliency value of the extracted protruding area by averaging the saliency of all the pixels therein;

将所得的显著性值表示为S p,对于初步认定为显著性的区域p,将其显著性值定义为式3: The resulting significance value is expressed as S p , and for the region p initially identified as significant, the significance value is defined as Equation 3:

Figure PCTCN2018091905-appb-000003
Figure PCTCN2018091905-appb-000003

其中,A(p)表示第p个区域中的像素数。Where A(p) represents the number of pixels in the p-th region.

3)最大值归一化;3) normalization of maximum value;

本发明利用地图统计来确定每个路径(步骤1)、2))的重要性;在最终整合阶段,结合两个路径的结果,在Maxima归一化之后对它们进行求和(MN)。The present invention utilizes map statistics to determine the importance of each path (steps 1), 2)); in the final integration phase, combining the results of the two paths, they are summed (MN) after Maxima normalization.

Maxima归一化算子N max(·)最初被提出用于整合来自多个特征通道(L.Itti,C.Koch and E.Niebur,"A model of saliency-based visual attention for rapid scene analysis,"in IEEE Transactions on Pattern Analysis and Machine Intelligence,vol.20,no.11,pp.1254-1259,Nov 1998.)的显著性图。 The Maxima normalization operator N max (·) was originally proposed for integration from multiple feature channels (L. Itti, C. Koch and E. Niebur, "A model of saliency-based visual attention for rapid scene analysis," In IEEE Profile on Pattern Analysis and Machine Intelligence, vol. 20, no. 11, pp. 1254-1259, Nov 1998.).

4)优化测地线技术,具体步骤如下:4) Optimize geodesic technology, the specific steps are as follows:

我们发现显著性值的权重可能对测地距离敏感。本发明采用一种可以更加均匀地增强突出物体区域的解决方案。首先根据线性频谱聚类方法将输入图像分割成多个超像素,并通过对其中所有像素的后验概率值Sp进行平均来计算每个超像素的后验概率。对于第j个超像素,如果其后验概率被标记为S(j),则第q个超像素的显著性值通过测地距离被改善如式4:We find that the weight of the significance value may be sensitive to the geodesic distance. The present invention employs a solution that can more evenly enhance the area of the protruding object. First, the input image is segmented into a plurality of superpixels according to a linear spectral clustering method, and the posterior probability of each superpixel is calculated by averaging the posterior probability values Sp of all the pixels therein. For the jth superpixel, if its posterior probability is marked as S(j), the significance value of the qth superpixel is improved by the geodesic distance as in Equation 4:

Figure PCTCN2018091905-appb-000004
Figure PCTCN2018091905-appb-000004

其中,J是超像素的总数;w qj将第q个超像素和第j个超像素之间测地距离的权重值。 Where J is the total number of superpixels ; wqj is the weighting value of the geodesic distance between the qth superpixel and the jth superpixel .

首先,已经有一个无向的权重图连接所有相邻的超像素(a k,a k+1),该无向图的权重d c(a k,a k+1)分配为他们的显著性值之间的欧几里得距离;然后,两者之间的测地距离超像素d g(p,i)可以定义为累积边图上最短路径的权重,表示为式5: First, there is already an undirected weight map connecting all adjacent superpixels (a k , a k+1 ), and the weights of the undirected graphs d c (a k , a k+1 ) are assigned to their significance. The Euclidean distance between the values; then, the geodetic distance between the two, the superpixel d g (p, i), can be defined as the weight of the shortest path on the cumulative edge graph, expressed as Equation 5:

Figure PCTCN2018091905-appb-000005
Figure PCTCN2018091905-appb-000005

然后将权重δ pi定义为式6: Then define the weight δ pi as Equation 6:

Figure PCTCN2018091905-appb-000006
Figure PCTCN2018091905-appb-000006

式6中,δ pi为第p个超像素和第i个超像素之间测地距离的权重值;σ c为d c的偏差;d g(p,j)为像素p和j之间的测地距离。 In Equation 6, δ pi is the weight value of the geodesic distance between the pth superpixel and the i th superpixel; σ c is the deviation of d c ; d g (p, j) is between pixels p and j Geodesic distance.

经过上述步骤,即检测得到全景图像的显著性。After the above steps, the saliency of the panoramic image is detected.

与现有技术相比,本发明的有益效果是:Compared with the prior art, the beneficial effects of the present invention are:

本发明提供一种利用区域增长算法和眼动模型进行全景图像的显著性检测的方法,首先采用基于区域生长的全景图像的空间密度模式检测方法来粗略提取初步对象。将眼固定模型嵌入到框架中,以预测视觉注意力;再通过最大值归一化将先前得到的显著性信息相融合,得出粗略的显著性图。最后,使用测地线优化技术来获得最终的显著性图。本发明能够解决现有方法的显著性检测精确度、健壮性不够,不适用于全景图片的问题,使全景图像中的显著性区域更精准地显现出来,为后期的目标识别和分类等应用提供精准且有用的信息。The invention provides a method for detecting the saliency of a panoramic image by using a region growing algorithm and an eye movement model. Firstly, a spatial density pattern detecting method based on a region-grown panoramic image is used to roughly extract a preliminary object. The eye-fixed model is embedded in the frame to predict visual attention; and the previously obtained saliency information is merged by maximum normalization to obtain a rough saliency map. Finally, geodesic optimization techniques are used to obtain the final saliency map. The invention can solve the problem that the saliency detection precision and the robustness of the prior method are insufficient, and is not suitable for the panoramic picture, so that the saliency area in the panoramic image is more accurately displayed, and provides for the later target recognition and classification applications. Precise and useful information.

与现有技术相比,本发明的技术优势体现为以下几方面:Compared with the prior art, the technical advantages of the present invention are embodied in the following aspects:

1)首次提出了一种基于组合区域生长和眼睛固定模型的全景图像的显著性检测模型。1) A saliency detection model for panoramic images based on combined region growth and eye fixation models was first proposed.

2)将区域生长的空间密度模式检测算法首次引入显著性检测领域。2) The spatial density pattern detection algorithm for regional growth is introduced into the field of significant detection for the first time.

3)构建了一种新的高品质全景数据集(SalPan),具有新颖的地面真实注释方法,可以消除显著物体的二义性。3) A new high-quality panoramic data set (SalPan) is constructed, which has a novel ground truth annotation method, which can eliminate the ambiguity of significant objects.

4)本发明所提出的模型也适用于常规图像的显著性检测。4) The model proposed by the present invention is also applicable to the saliency detection of a conventional image.

5)本发明方法还可有助于在广泛的视野中找出人类视觉系统对于大尺度视觉内容的感知特征。5) The method of the present invention can also help to find the perceptual characteristics of the human visual system for large-scale visual content in a wide field of view.

附图说明DRAWINGS

图1为本发明提供的检测方法的流程框图。FIG. 1 is a flow chart of a detection method provided by the present invention.

图2为本发明实施例中采用的输入全景图像、其他方法检测图像、本发明检测图像,以及人工标定想要得到的图像;2 is an input panoramic image, another method detection image, a detection image of the present invention, and an artificially calibrated image to be obtained according to an embodiment of the present invention;

其中,第一行为输入图像;第二至第六行为现有其他方法得到的检测结果图像;第七行为本发明检测结果图像;第八行为人工标定期望得到的图像。Wherein, the first behavior input image; the second to sixth behaviors are the detection result images obtained by other methods; the seventh behavior is the detection result image of the present invention; and the eighth behavior is to manually calibrate the desired image.

图3为本发明适用于常规图像的显著性检测效果图;3 is a diagram showing the effect of saliency detection applied to a conventional image according to the present invention;

其中,第一行为输入常规图像,第二行为本发明检测结果图像,第三行为人工标定期望得到的图像。Wherein, the first behavior inputs a regular image, the second behavior is a detection result image of the present invention, and the third behavior manually calibrates the desired image.

具体实施方式Detailed ways

下面结合附图,通过实施例进一步描述本发明,但不以任何方式限制本发明的范围。The invention is further described by the following examples in conjunction with the accompanying drawings, but not by way of limitation.

本发明提供一种利用区域增长算法和眼动模型进行全景图像的显著性检测的方法,首先采用基于区域生长的全景图像的空间密度模式检测方法来粗略提取初步对象。将眼固定模型嵌入到框架中,以预测视觉注意力;再通过最大值归一化将先前得到的显著性信息相融合,得出粗略的显著性图。最后,使用测地线优化技术来获得最终的显著性图,实验对比图如图2所示。The invention provides a method for detecting the saliency of a panoramic image by using a region growing algorithm and an eye movement model. Firstly, a spatial density pattern detecting method based on a region-grown panoramic image is used to roughly extract a preliminary object. The eye-fixed model is embedded in the frame to predict visual attention; and the previously obtained saliency information is merged by maximum normalization to obtain a rough saliency map. Finally, using the geodesic optimization technique to obtain the final saliency map, the experimental comparison is shown in Figure 2.

图1为本发明提供的显著性检测方法的流程框图,包括四个主要步骤。首先,我们采用区域增长算法进行显著性物体区域的自动框选。其次,使用眼固定预测模型估计显著点。然后,利用最大值归一化方法融合先前显著性信息。最后,通过测地线优化技术获得最后的显著性检测结果图。详细过程阐述如下:FIG. 1 is a block diagram of a saliency detection method provided by the present invention, which includes four main steps. First, we use the region growing algorithm to automate the selection of significant object regions. Second, use the fixed-eye prediction model to estimate significant points. The previous significance information is then fused using the maximum normalization method. Finally, the final significance test results are obtained by geodesic optimization techniques. The detailed process is described as follows:

步骤一、基于区域增长的检测。Step 1. Detection based on regional growth.

在本步中,我们的目标是粗略地提取与其邻居相比具有显著不同密度的区域。我们认为,重大差异的区域可以分为三类:1)过密度,2)密度不足,3)由山脊或沟渠包围的地区。开 始时,将原始图像分割成M*N个区域,并转换成密度矩阵,其中每个单位(i,j)表示第(i,j)个小区内的对象的计数。基于作为强度图像处理的该密度矩阵,应用诸如图像形态算子和增强技术的图像处理技术,然后应用基于区域增长的算法来提取显著不同的区域。相比使用其他技术,仅输出粗糙的矩形边界框,该算法可以返回明显不同区域的精确形状。为了简单起见,我们将原始彩色图像转换为灰度图像,然后将对象提案算法应用于灰度图像。因此,所得到的图像可以被看作是密度图。区域增长涉及的一些问题如下:(a)提高密度图像。我们应用形态学操作,包括形态学扩张,侵蚀,开放和近距离,以消除像非常小的区域之类的噪声,并且连接彼此靠近的单独的同质区域。(b)排除不同的背景地区。一些提示用于后处理步骤,例如平均强度值和提取区域的总面积以排除不良结果。(c)种子选择。在实施过程中,自动种子选择和迭代提供阈值。自动选择似乎取得了良好的效果,因此在拟议方法中被采用为种子选择方法。(d)阈值。选用自适应阈值处理。实验结果表明,基于区域增长的算法在检测具有有效计算能力的重要区域中运行良好。通过估计密度矩阵,我们可以提出一些显著的区域,可以在下一步中加强或重新估计该区域的显著性。In this step, our goal is to roughly extract areas of significantly different density compared to their neighbors. We believe that areas of significant difference can be divided into three categories: 1) overdensity, 2) insufficient density, and 3) areas surrounded by ridges or ditches. Initially, the original image is segmented into M*N regions and converted into a density matrix, where each unit (i, j) represents the count of objects within the (i, j)th cell. Based on the density matrix as intensity image processing, image processing techniques such as image morphological operators and enhancement techniques are applied, and then region growing based algorithms are applied to extract significantly different regions. Compared to other techniques that only output a rough rectangular bounding box, the algorithm can return the exact shape of a distinctly different area. For the sake of simplicity, we convert the original color image into a grayscale image and then apply the object proposal algorithm to the grayscale image. Therefore, the resulting image can be regarded as a density map. Some of the issues involved in regional growth are as follows: (a) Increased density images. We apply morphological operations, including morphological expansion, erosion, openness, and close proximity to eliminate noise like very small areas and connect separate homogeneous regions that are close together. (b) Exclude different background areas. Some hints are used for post-processing steps such as average intensity values and total area of the extraction area to rule out poor results. (c) Seed selection. In the implementation process, automatic seed selection and iteration provide thresholds. Automatic selection seems to have achieved good results and was therefore adopted as a seed selection method in the proposed method. (d) Threshold. Use adaptive thresholding. The experimental results show that the algorithm based on region growth works well in detecting important areas with effective computing power. By estimating the density matrix, we can propose some significant regions that can be enhanced or re-estimated in the next step.

步骤二、眼动固定点预测。Step 2: Eye movement fixed point prediction.

一个位置是否显著,在很大程度上取决于它吸引人们的注意力。眼睛固定预测的大量近期工作已经或多或少地显露出来这个问题的性质。眼固定预测模型模拟人类视觉系统的机制,从而可以预测一个位置吸引人们注意的概率。所以在本步中,我们使用眼固定模型来帮助我们确保哪个区域会更加吸引人们的注意力。全景图像通常具有宽视野,因此与常规图像相比计算上更昂贵。基于颜色对比的算法,局部信息不适合作为全景图像的预处理步骤,因为这些算法是耗时且花费大量计算资源的。因此,本发明采用一种更有效的方法来帮助我们快速扫描图像,并粗略地定位吸引人们关注的地方。频域中的固定预测模型在计算上有效且易于实现,因此,本发明采用频域中的眼动预测模型为签名模型。签名模型通过取变换域中的混合信号X的符号大致隔离前景的空间支持,然后将其转换回空间域,即通过计算重构图像

Figure PCTCN2018091905-appb-000007
表示X的DCT变换。图像签名IS(X)定义为式1: Whether a location is significant depends largely on its ability to attract attention. A large amount of recent work on eye fixation predictions has more or less revealed the nature of this problem. The fixed-eye prediction model simulates the mechanisms of the human visual system so that it can predict the probability that a location will attract attention. So in this step, we use eye-fixed models to help us ensure which areas are more attractive. Panoramic images typically have a wide field of view and are therefore computationally more expensive than conventional images. Based on the color contrast algorithm, local information is not suitable as a pre-processing step for panoramic images because these algorithms are time consuming and costly computationally intensive. Therefore, the present invention employs a more efficient method to help us scan images quickly and roughly locate where attention is drawn. The fixed prediction model in the frequency domain is computationally efficient and easy to implement. Therefore, the present invention uses the eye movement prediction model in the frequency domain as the signature model. The signature model roughly isolates the spatial support of the foreground by taking the sign of the mixed signal X in the transform domain, and then converts it back into the spatial domain, ie by reconstructing the reconstructed image
Figure PCTCN2018091905-appb-000007
Indicates the DCT transform of X. The image signature IS(X) is defined as Equation 1:

IS(X)=sign(DCT(X))                (式1)IS(X)=sign(DCT(X)) (Formula 1)

其中,sign()为符号函数,DCT()为DCT变换函数。Where sign() is a symbol function and DCT() is a DCT transform function.

显著性图是通过平滑上面定义的平方重建图像形成的,表示为式2。The saliency map is formed by smoothing the squared reconstructed image defined above, expressed as Equation 2.

Figure PCTCN2018091905-appb-000008
Figure PCTCN2018091905-appb-000008

其中,g表示高斯内核。Where g is the Gaussian kernel.

图像签名是一个简单而强大的自然场景描述符,可用于近似隐藏在光谱稀疏背景中的稀疏前景的空间位置。与其他眼固定模型相比,图像签名具有更高效的实现,运行速度快于所有其他方法。为了将上一步中提出的突出区域与图像签名产生的显著性图像S m进行组合,我们通过对其中所有像素的显著性进行平均值来分配所提出的突出区域的显著性值。为方便起见,我们将所得的显著性图表示为S p。也就是说,对于初步标记为显著的区域p,其显著性值被定义为式3: Image Signature is a simple and powerful natural scene descriptor that can be used to approximate the spatial location of a sparse foreground hidden in a spectrally sparse background. Compared to other fixed-eye models, image signatures are more efficient and run faster than all other methods. In order to combine the salient regions proposed in the previous step with the salient images S m generated by the image signature, we assign the saliency values of the proposed salient regions by averaging the saliency of all the pixels therein. For convenience, we represent the resulting saliency map as S p . That is, for a region p that is initially marked as significant, its significance value is defined as Equation 3:

Figure PCTCN2018091905-appb-000009
Figure PCTCN2018091905-appb-000009

其中,A(p)表示第p个区域中的像素数。Where A(p) represents the number of pixels in the p-th region.

步骤三、最大值归一化。Step 3: The maximum value is normalized.

融合多个模型的显着性检测结果被认为是一项具有挑战性的任务,因为候选模型通常是基于不同的提示或假设而开发的。幸运的是,在我们的案例中,整合问题比较容易,因为我们只考虑两个路径的输出。既然没有先前的知识或其他的可以使用自上而下的指导,利用地图统计来确定每个路径的重要性更安全。在最终整合阶段,我们结合两个路径的结果,在Maxima归一化之后对它们进行求和(MN)。Maxima归一化算子N max(·)最初被提出用于整合来自多个特征通道(L.Itti,C.Koch and E.Niebur,"A model of saliency-based visual attention for rapid scene analysis,"in IEEE Transactions on Pattern Analysis and Machine Intelligence,vol.20,no.11,pp.1254-1259,Nov 1998.)的显著性图。 The saliency detection results of merging multiple models are considered to be a challenging task because candidate models are usually developed based on different cues or assumptions. Fortunately, in our case, the integration problem is easier because we only consider the output of the two paths. Since there is no prior knowledge or other top-down guidance, it is safer to use map statistics to determine the importance of each path. In the final integration phase, we combine the results of the two paths and summon them (MN) after Maxima normalization. The Maxima normalization operator N max (·) was originally proposed for integration from multiple feature channels (L. Itti, C. Koch and E. Niebur, "A model of saliency-based visual attention for rapid scene analysis," In IEEE Profile on Pattern Analysis and Machine Intelligence, vol. 20, no. 11, pp. 1254-1259, Nov 1998.).

步骤四、测地线技术优化。Step 4: Geodesic technology optimization.

我们提出的方法的最后一步是采用测地距离,进行最终结果的优化。首先根据线性频谱聚类方法将输入图像分割成多个超像素,并通过对其中所有像素的后验概率值Sp进行平均来计算每个超像素的后验概率。对于第j个超像素,如果其后验概率被标记为S(j),则第q个超像素的显著值通过测地距离被改善如式4:The final step in the proposed method is to use the geodesic distance to optimize the final result. First, the input image is segmented into a plurality of superpixels according to a linear spectral clustering method, and the posterior probability of each superpixel is calculated by averaging the posterior probability values Sp of all the pixels therein. For the jth superpixel, if its posterior probability is marked as S(j), the significant value of the qth superpixel is improved by the geodesic distance as in Equation 4:

Figure PCTCN2018091905-appb-000010
Figure PCTCN2018091905-appb-000010

其中,J是超像素的总数,w qj将是基于测地距离的权重在第q个超像素和第j个超像素之间。首先,已经有一个无向的权重图连接所有相邻的超像素(a k,a k+1)并将其重量d c(a k,a k+1)分配为他们的显著性值之间的欧几里得距离。 Where J is the total number of superpixels , and wqj will be based on the weight of the geodesic distance between the qth superpixel and the jth superpixel. First, there is already an undirected weight map connecting all adjacent superpixels (a k , a k+1 ) and assigning their weight d c (a k , a k+1 ) between their significance values. Euclidean distance.

然后,两者之间的测地距离超像素d g(p,i)可以定义为累积边图上最短路径的权重,表示为式5: Then, the geodetic distance superpixel d g (p, i) between the two can be defined as the weight of the shortest path on the cumulative edge graph, expressed as Equation 5:

Figure PCTCN2018091905-appb-000011
Figure PCTCN2018091905-appb-000011

以这种方式,可以得到任何两个之间的测地距离图像中的超像素。In this way, superpixels in the geodetic distance image between any two can be obtained.

然后将权重δ pi定义为式6: Then define the weight δ pi as Equation 6:

Figure PCTCN2018091905-appb-000012
Figure PCTCN2018091905-appb-000012

式6中,δ pi为第p个超像素和第i个超像素之间测地距离的权重值;σ c为d c的偏差;d g(p,j)为像素p和j之间的测地距离。 In Equation 6, δ pi is the weight value of the geodesic distance between the pth superpixel and the i th superpixel; σ c is the deviation of d c ; d g (p, j) is between pixels p and j Geodesic distance.

通过以上步骤,我们能够得到最终的显著性检测结果图,实验对比图如图2所示。同时,本发明方法也适用于常规尺寸的图片,实验效果图如图3所示。Through the above steps, we can get the final saliency test results, the experimental comparison chart is shown in Figure 2. At the same time, the method of the invention is also applicable to pictures of conventional size, and the experimental effect diagram is shown in FIG.

需要注意的是,公布实施例的目的在于帮助进一步理解本发明,但是本领域的技术人员可以理解:在不脱离本发明及所附权利要求的精神和范围内,各种替换和修改都是可能的。因此,本发明不应局限于实施例所公开的内容,本发明要求保护的范围以权利要求书界定的范围为准。It is to be noted that the embodiments are disclosed to facilitate a further understanding of the invention, but those skilled in the art can understand that various alternatives and modifications are possible without departing from the spirit and scope of the invention and the appended claims. of. Therefore, the invention should not be limited by the scope of the invention, and the scope of the invention is defined by the scope of the claims.

Claims (5)

一种基于区域增长和眼动模型的全景图像显著性检测方法,使用区域生长和固定预测模型,实现全景图像的自动突出物体检测;包括如下步骤:A method for detecting panoramic image saliency based on regional growth and eye movement model, using region growing and fixed prediction models to realize automatic protruding object detection of panoramic images; the following steps are included: 1)针对原始图像进行基于区域增长的检测,通过区域增长算法粗略提取与其邻居相比具有显著不同密度的区域,得到密度重大差异区域,即突出区域;1) Performing region-based growth detection on the original image, and roughly extracting regions having significantly different densities compared with their neighbors by the region growing algorithm, and obtaining regions with significant density differences, that is, protruding regions; 2)通过眼动固定点预测,得到突出区域的显著性值;包括如下步骤:2) Obtaining the salient value of the highlighted area by the fixed point prediction of the eye movement; the following steps are included: 21)使用眼固定模型进行分析,得到显著性区域;21) using an eye-fixed model for analysis to obtain a significant region; 22)采用频域中的固定预测模型快速扫描图像,并粗略地定位吸引人们关注的地方;22) Using a fixed prediction model in the frequency domain to quickly scan the image and roughly locate the places that attract people's attention; 23)采用签名模型,通过计算重构图像
Figure PCTCN2018091905-appb-100001
表示X的DCT变换;X为变换域中的混合信号;签名模型被定义为IS(X),表示为式1:
23) Using a signature model to reconstruct images by calculation
Figure PCTCN2018091905-appb-100001
Indicates the DCT transform of X; X is the mixed signal in the transform domain; the signature model is defined as IS(X), expressed as Equation 1:
IS(X)=sign(DCT(X))    (式1)IS(X)=sign(DCT(X)) (Formula 1) 通过平滑重建图像形成显著性图像S m,表示为式2: A saliency image S m is formed by smooth reconstruction of the image, expressed as Equation 2:
Figure PCTCN2018091905-appb-100002
Figure PCTCN2018091905-appb-100002
其中,g表示高斯内核;Where g is the Gaussian kernel; 24)将提取出的突出区域与图像签名产生的显著性图像S m进行组合,通过对其中所有像素的显著性进行平均,分配所提取出的突出区域的显著性值; 24) combining the extracted protruding area with the saliency image S m generated by the image signature, and averaging the saliency of all the pixels therein, and assigning the saliency value of the extracted protruding area; 3)进行最大值归一化后求和;3) summing after the maximum value is normalized; 4)采用优化测地线方法,使得更均匀地增强突出区域,具体步骤如下:4) Using the optimized geodesic method to make the protruding area more uniform, the specific steps are as follows: 首先根据线性频谱聚类方法将输入图像分割成多个超像素,并通过对其中所有像素的后验概率值Sp进行平均来计算每个超像素的后验概率;对于第j个超像素,如果其后验概率被标记为S(j),则第q个超像素的显著值通过测地距离被优化如式4:First, the input image is segmented into a plurality of superpixels according to a linear spectral clustering method, and the posterior probability of each superpixel is calculated by averaging the posterior probability values Sp of all the pixels; for the jth superpixel, if The posterior probability is marked as S(j), and the significant value of the qth superpixel is optimized by the geodesic distance as shown in Equation 4:
Figure PCTCN2018091905-appb-100003
Figure PCTCN2018091905-appb-100003
其中,J是超像素的总数;w qj将第q个超像素和第j个超像素之间测地距离的权重值; Where J is the total number of superpixels ; wqj is the weighting value of the geodesic distance between the qth superpixel and the jth superpixel ; 已有一个无向的权重图连接所有相邻的超像素(a k,a k+1),该无向图的权重d c(a k,a k+1)分配为其显著性值之间的欧几里得距离;将两者之间的测地距离超像素d g(p,i)定义为累积边图上最短路径的权重,表示为式5: There is an undirected weight map connecting all adjacent superpixels (a k , a k+1 ), and the weight of the undirected graph d c (a k , a k+1 ) is assigned between its significance values. The Euclidean distance; the geodetic distance superpixel d g (p, i) between the two is defined as the weight of the shortest path on the cumulative edge graph, expressed as Equation 5:
Figure PCTCN2018091905-appb-100004
Figure PCTCN2018091905-appb-100004
然后,将权重δ pi定义为式6: Then, the weight δ pi is defined as Equation 6:
Figure PCTCN2018091905-appb-100005
Figure PCTCN2018091905-appb-100005
式6中,δ pi为第p个超像素和第i个超像素之间测地距离的权重值;σ c为d c的偏差;d g(p,j)为像素p和j之间的测地距离; In Equation 6, δ pi is the weight value of the geodesic distance between the pth superpixel and the i th superpixel; σ c is the deviation of d c ; d g (p, j) is between pixels p and j Geodesic distance 经过上述步骤,即检测得到全景图像的显著性。After the above steps, the saliency of the panoramic image is detected.
如权利要求1所述全景图像显著性检测方法,其特征是,步骤1)中,密度重大差异区域包括:过密度的区域、密度不足的区域、由山脊或沟渠包围的地区;提取过程包括如下步骤:The panoramic image saliency detecting method according to claim 1, wherein in step 1), the region of significant difference in density comprises: an area of excessive density, an area of insufficient density, an area surrounded by a ridge or a ditch; and the extraction process includes the following step: 11)开始时,将原始图像分割成M*N个小区域,并转换成密度矩阵,其中每个单位(i,j)表示第(i,j)个小区域内的对象的计数;对原始图像经过密度矩阵的处理,得到强度图像;11) At the beginning, the original image is segmented into M*N small regions and converted into a density matrix, where each unit (i, j) represents the count of objects in the (i, j) small regions; Through the processing of the density matrix, an intensity image is obtained; 12)基于密度矩阵,应用图像处理方法进行图像增强,再应用基于区域增长的算法来提取显著不同的区域,得到明显不同区域的精确形状,仅输出粗糙的矩形边界框。12) Based on the density matrix, the image processing method is applied to enhance the image, and then the region growing algorithm is applied to extract significantly different regions, and the precise shapes of the distinct regions are obtained, and only the rough rectangular bounding box is output. 如权利要求2所述全景图像显著性检测方法,其特征是,将原始彩色图像转换为灰度图像,然后将对象提案算法应用于灰度图像,所得到的图像看作为密度图;采用基于区域增长的算法提取突出区域的过程中,应用形态学操作方法消除噪声,并且连接彼此靠近的单独的同质区域,以提高密度图像;采用优化方法排除不良结果,以排除不同的背景地区;采用种子选择方法,在实施过程中,自动种子选择和迭代提供阈值;阈值选择选用自适应阈值处理。A panoramic image saliency detecting method according to claim 2, wherein the original color image is converted into a grayscale image, and then the object proposal algorithm is applied to the grayscale image, and the obtained image is regarded as a density map; In the process of extracting the salient region, the morphological operation method is used to eliminate the noise, and the separate homogenous regions close to each other are connected to increase the density image; the optimization method is used to eliminate the bad results to exclude different background regions; The selection method, in the implementation process, automatic seed selection and iteration provides a threshold; the threshold selection uses adaptive threshold processing. 如权利要求1所述全景图像显著性检测方法,其特征是,步骤24)中,获得突出区域的显著性值,具体将所得的显著性图表示为S p,对于初步认定为显著性的区域p,将其显著性值定义为式3: The panoramic image saliency detecting method according to claim 1, wherein in step 24), the saliency value of the protruding region is obtained, and the obtained saliency map is specifically expressed as S p , for the region initially identified as significant. p, define its significance value as Equation 3:
Figure PCTCN2018091905-appb-100006
Figure PCTCN2018091905-appb-100006
其中,A(p)表示第p个区域中的像素数。Where A(p) represents the number of pixels in the p-th region.
如权利要求1所述全景图像显著性检测方法,其特征是,步骤3)进行最大值归一化,具体采用Maxima归一化,在Maxima归一化之后进行求和。The panoramic image saliency detecting method according to claim 1, wherein the step 3) performs maximum normalization, specifically using Maxima normalization, and summing after Maxima normalization.
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