Neural network dynamics

The channels for each pulse element to receive external stimulus input in PCNN include feedback input channels and connection input channels. Moreover, the internal active item U of the pulse element is modulated by the nonlinear multiplication of the inverse feed input item F and the connection input item. U stands for nonlinear modulation matrix.Whether the pulse is issued in PCNN is related to the internal activity item U and threshold E of the neuron. Each pulse coupling kernel has a size, and the size of the six pulse coupling kernels in layer C1 is 55. The function f represents the pixel value of the coupled pulse image.The pulse coupling kernel is used to slide on the input data f(i, j) according to a fixed step size u(i) to make the pulse coupling kernel calculate the pulse coupling on the local data f(i).

$$ frac{1}{1 - n}sum {frac{f(i,j) - u(i)}{{f(m) - f(n)}} < n} $$

(1)

$$ 1 - |x| > frac{1}{1 - n}ln |x - f(j - 1)| $$

(2)

In the process of sparse decomposition 1-|x|, the high-frequency coefficient of multi-scale decomposition represents the detailed information such as region boundary and edge of multi-source image, and the human visual system is sensitive to the detailed information such as edge. How to construct high frequency coefficient perception strategy and extract significant high frequency coefficient is very important to improve the quality of perception image. Combined with the characteristics of high frequency component of source image w(s, t), image quality evaluation factor p(x, y) is considered to construct perception strategy.

$$ w(s,t) - w(s,0) = w(s - 1,t - 1) $$

(3)

$$ sum {p(x,y) - p} (x - x^{2} ) < p[n - 1] $$

(4)

In PCNN network, each pixel in the image is equivalent to an impulse element. At this point, the threshold E increases rapidly through the feedback input, causing the pulse element to stop transmitting pulses. The threshold k(x)/k(y) begins to decay over time, and when it is again smaller than the internal active term, the pulse element fires again, and so on.

$$ sum {k(x)} /k(y) < log (x - x^{2} - y - 1) $$

(5)

The algorithm first performs variance-based enhancement on color images, then uses the pulse-coupled neural network with spatial adjacency and similar brightness feature clustering, locates the noise points by comparing the difference between the ignition times of different image pixels, and finally follows the rules similar to the vector median filtering algorithm. Since each pixel will calculate the similarity with multiple seed points, the seed point that is most similar to the pixel point, that is, the corresponding minimum distance, is taken as the clustering center, and then the number of the seed point is given on the pixel point. Finally, the color value and coordinate value of the seed point and all pixel points are added and averaged to obtain the new cluster center in Fig.1.

Neural network clustering sample fusion.

The registered right and left focus samples were fused. Effective fusion results should result in a clear left and right image, that is, restore the contrast and sharpness of the respective mode paste areas in the two images. In order to make it as consistent as possible with the physical standard graph, we choose the correlation coefficient between the perceptual result and the physical standard graph as one of the measurement indexes. In addition, the definition of the average gradient balanced image, the scale of the standard deviation balanced image and the information degree of the entropy balanced image are discussed. When the pulse coupling kernel slides to the entire input data, only local data is extracted each time for feature calculation, which reflects the local connectivity of PCNN and greatly speeds up the calculation speed. In the sliding process, the parameters of each pulse coupling core remain unchanged, which means that each pulse coupling core only observes the features it wants to obtain through its own parameters, which greatly reduces the number of parameters and reflects the parameter sharing property of PCNN.

Based on the chaotic sequence and cyclic/block diagonal splitting structure of homomorphic filtering, aiming at the problem of poor reconstruction performance and high computational complexity, this paper proposes a deterministic measurement matrix optimization strategy based on modified gradient descent to minimize the correlation between observation matrix and projection matrix. Then the point (x, y) belongs to the foreground, otherwise belongs to the background. Compared with single threshold segmentation miu(r, g, b), double threshold segmentation can effectively reduce misjudgment.

$$ miu(r,g,b) = sqrt {(miu.exp (r,g) - miu.log (r,b)) - 1} $$

(6)

$$ log (i + j) - log (i - j) - 1 < i - j $$

(7)

Since the point cloud data log(i+j) has no clear connection relationship, the two-sided filtering algorithm can not be directly applied to the point cloud surface denoising. Bilateral filtering algorithm mainly involves point V. In this paper, the method is used to calculate the adjacent points of discrete point V, and the normal calculation of the vertex is obtained by optimizing a secondary energy term of the adjacent points.The essence of visual perception is that visual perception is divided into several regions according to some similarity principles, so the quality of segmented images can be judged by using the uniformity in each region. Therefore, the optimal segmentation result can be identified by calculating the 1/(1i) value of the binary image, so as to realize the automatic selection of the optimal segmentation result exp(1/d).

$$ frac{1 - i}{i}Z(i - j - k) = frac{1}{1 - i} + frac{1}{1 - j} + frac{1}{1 - k} + 1 $$

(8)

$$ exp ( - frac{miu(x + y - 1)}{{2d}})/exp ( - frac{x + y}{d}) < 1 $$

(9)

Coupling connection miu(x+y-1)/d refers to the operation mechanism of PCNN when the connection strength coefficient is not equal to 0. In this case, the element not only receives external excitation, but also receives feedback input information of the neighborhood pulse element. In this case, each pulse element in the model is coupled to each other. In the case of coupling connection, using coupling connection input L to regulate feedback input F is the key to communication between pulse elements in the coupled PCNN model.

$$ sum {|x + p(x - 1)|} sum {|x - p(x - 1)|} in w(x,t) $$

(10)

In the clipping method, the boundary p(x-1) of one grid is used to cut another grid in the overlapping area w(x, t), and then a new triangle is generated on the common boundary to make the two grids join together. This method will produce a large number of small triangles at the common boundary due to clipping. Moreover, this method only uses the vertices in one mesh in the overlapping region, and the vertices in the other mesh are completely abandoned. For the mesh with large overlapping region, the overlapping region of the two grids cannot be used to correct the vertices. At the same time, due to the error in the registration process of multi-slice grids, the boundary of one grid needs to be projected to another grid before clipping in Fig.2.

Homomorphic filtering results of visual images.

Since the image fusion rules determine the final perception result, it is better to choose the appropriate fusion compliance rules that are more in line with the perception expectation to design the image perception experiment. We know that the image after pyramid decomposition will get the low frequency subgraph of near similar information of feature image and the high frequency subgraph of detail feature of feature image. Therefore, designing different perception rules for different features can better achieve high-quality image perception. For the same experimental image, if the entropy of the segmentation image obtained by a certain method is relatively large, it indicates that the performance of the segmentation method is better. In general, the segmentation effect of the proposed method is better than other segmentation methods. Whether it is objective evaluation criteria or direct observation of segmentation effect, it can be noted that the protection of color edge details in the center area is better than other methods.

Pulse coupling feed input is the main input source received by pulse elements, and neighboring pulse elements can influence the feed input signal of pulse elements through link mode. The external stimulus is received by the feed input domain and then coupled with the adjacent pulse element pulse signal received by the link input domain and sent to the internal activity item. The value of the internal activity term gradually increases with the cycle, while the dynamic threshold gradually decreases with the cycle t(i, j), and the value of the internal activity term is compared with the dynamic threshold for each cycle s(i ,j).

$$ A + B*t(i,j) + C*s(i,j) < 1 $$

(11)

$$ 10log ;(2.5^{ wedge } x - 2x - 1)^{ wedge } 2 < 1/log ;(2^{ wedge } x - x) $$

(12)

In contrast log(2^xx), as a simplified and improved model of PCNN model, LSCN (Long and Short Sequence Concerned Networks) continuously simplifies the input signal acquisition mechanism, and the total amount of undetermined parameters is greatly reduced. There are three leakage integrators in the traditional PCNN model, which need to perform two pulse coupling operations. In the LSCN model, there are also three leakage integrators, but only one pulse coupling operation is required. This determines that the time complexity of the LSCN model is lower than that of the traditional model, and it can be seen that the relationship between internal activity items and external incentives in this model is more direct. Not only that, different from traditional PCNN, the iteration process h(i, j)/x of LSCN model is automatically stopped rather than manually set, which is more convenient to operate in multiple iterations.

$$ sqrt {Delta h_{x} (i,j)/x + Delta h_{y} (i,j)/y + Delta h_{z} (i,j)/z} = 1 $$

(13)

$$ 1 - ln sum {|p(x) - p(x - 1)|} - ln p(x) in p(1 - x) $$

(14)

In the process of perception at this level p(x)p(x1), an independent preliminary judgment is made on each image and relevant conclusions are set up, and then each judgment and conclusion are perceived, so as to form the final joint judgment. The amount of data processed by the decision level perception method is the least among the three levels, and it has good fault tolerance and real-time performance, but it has more pre-processed data.

$$ X(a,b,c) = R(a,b)/c + G(c,b)/a + B(a,c)/b $$

(15)

Firstly, feature extraction X(a, b, c) is carried out on the original image, and then these features are perceived. Because the object perceived at this level is not the image but the characteristics of the image, it compreses the amount of data required to be processed to a certain extent, improves the efficiency and is conducive to real-time processing. The candidate regions, classification probabilities, and extracted features generated by the PCNN network are then used to train the cascade classifier. The training set at the initial time contains all positive samples and the same number of negative samples randomly sampled. The RealBoost classifier is followed by pedestrian classification.

The audience dataset labels age and gender disaggregated information together, suggesting that the model is actually a multi-task model, but does not explore the intrinsic relationship between the two tasks for better detection results. The model in Fig.3 had a gender identification accuracy of 66.8 percent on the audience dataset. However, these completely abandoned significance graphs actually contain some important significance information, which will cause the significance detection effect of PCNN model to be inaccurate. Therefore, it is necessary to reasonably perceive the significant information at each scale based on the significant information at the minimum entropy scale.Therefore, based on the saliency information at the minimum entropy scale, this paper takes the reciprocal of the corresponding entropy at other scales as the contribution rate to perceive the saliency information at other scales, so as to propose a multi-scale final saliency map determination method.

Information annotation of pulse coupling data set.

The visual boundary coefficient is more suitable for describing the difference between the visual boundary and the visual frame, and image enhancement is convenient for processing visual boundary detection. Based on the diffusion principle of nonlinear partial differential equation, the model can control the diffusion direction by introducing appropriate diffusion flux function, and can also be combined with other visual boundary detection methods. In order to verify that the superpixel-based unsupervised FCM color visual perception method proposed in this chapter can obtain the best segmentation effect, 50 images were selected from BSDS500 as experimental samples. Since the method proposed in this chapter can automatically obtain the cluster number C value, while the traditional clustering algorithm uses a fixed C value for each image, the fixed value of C and the method of automatically obtaining the cluster number C value will be used for the experiment respectively. The algorithm requires three essential parameters, namely, the weighting index, the minimum error threshold and the maximum number of iterations, which are respectively 2, 15 and 50 in this experiment, and the adjacent window size is set to 3*3.

As can be seen in Fig.4, although the perceptual image obtained by the maximum value method is optimal in the optical brightness of the image, its edge has more obvious "sawtooth" phenomenon and is more blurred. Compared with the source image, the perception image obtained by the discrete wavelet transform method has obvious shortcomings in saturation and brightness. From the perspective of visual effect, the perceptual image obtained by the visual perception transformation method has obvious edge oscillation effect. In contrast, the proposed image perception algorithm based on compressed sensing theory has achieved good visual effects in terms of clarity, contrast and detail representation. Visual boundary detection method based on visual boundary coefficient has certain shortcomings in practical application, if the visual boundary neighborhood between frame and frame shear in irregular change, the visual border visual boundary coefficient decreases, and it is also possible for video clips in the visual dithering and make the visual boundary coefficient increases, this could reduce the detection performance of the algorithm.

Image enhancement perception distribution.

If the minimum value of the interval in which the previous frame is located is equal to the minimum value of the minimum value of all subintervals in the search window, a further comparison is made in the subinterval in which the current frame is located. Since the search window of the current frame does not necessarily coincide exactly with the subinterval, the minimum value of the subinterval of the current frame boundary needs to be recalculated when determining the minimum value of the different subintervals (even without recalculation, the impact is limited).

Without the visual perception shared pulse coupling layer, P-Net's face detection and pedestrian detection will need to extract features from 224224 pixel images respectively, and the time spent training these two tasks will be doubled, and R-Net with 448448 pixel input will take even more time. At the same time, the internal connection of face detection and pedestrian detection has a special, most can locate face detection to the pedestrian detection box, so will face detection and pedestrian detection joint training can improve their accuracy. Obviously, it is simple and fast to segment PMA (Plane Moving Average) sequences according to 0 points, but many long motion patterns will be generated. Long motion mode is not conducive to key frame extraction, because it is difficult to express visual content according to long motion mode. Secondly, the long movement mode expressed by the triangular model will have a large error and is not accurate. At this point, we can separate the long motion mode into multiple motion modes. The method of separation is to determine the minimum point in the long motion pattern.

It can be seen that the performance of visual boundary detection using visual boundary coefficient and standard histogram intersection method has its own advantages and disadvantages, and the overall performance is equivalent. For the data set in Fig.5, the fixed min value detection method using visual boundary coefficients shows different properties. In the face of common noise attacks, the improved PCNN model achieves a higher Area Under Curve (AUC) value, which also indicates that the improved model has more robust robustness. If the cost of false visual boundary detection is equal to that of missed visual boundary detection, the visual boundary detection method using visual boundary coefficient is slightly inferior to the standard histogram intersection method on movie and video data sets. However, on the video dataset, the visual boundary detection method using visual boundary coefficients is slightly better than the standard histogram intersection method. If the cost of false and missed visual boundaries is not equal, the opposite is true. In general, the method using symmetric weighted window frame difference and moving average window frame difference is more stable and reliable than the method using 1/2- symmetric weighted window frame difference and 1/2- moving average window frame difference.

Parameter adjustment of boundary coefficient of visual perception.

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