Max Filter Research Articles

Group-Invariant Max Filtering

AbstractGiven a real inner product space V and a group G of linear isometries, we construct a family of G-invariant real-valued functions on V that we call max filters. In the case where $$V={\mathbb {R}}^d$$ V = R d and G is finite, a suitable max filter bank separates orbits, and is even bilipschitz in the quotient metric. In the case where $$V=L^2({\mathbb {R}}^d)$$ V = L 2 ( R d ) and G is the group of translation operators, a max filter exhibits stability to diffeomorphic distortion like that of the scattering transform introduced by Mallat. We establish that max filters are well suited for various classification tasks, both in theory and in practice.

Car-Plate Image Enhancement by Using Median and Max Filters


 
 
 
 Nowadays, Optical Character recognition is one of the affected tools for recognition the plate of car from a still video or image in the intelligent transportation systems. The Optical Character Recognition accuracy incompletely depends on the input image quality. In this article, two efficient approaches are proposed to enhance the quality of the car plate image selected from video clips. To minimize the error rate the proposed technique is used even at low resolution image. Maximum, and median filters are used in this work to enhance the quality of image. These technique extend to collect the pixels of the consecutive frames of the video in filtering approaches. The error rate of the OCR is tested on fifty road and street video clips by decreasing the resolution of the images and filtering them with common and proposed filtering methods. The test results indicate that both proposed methods, improve the accuracy of OCR, and the highest reduction of error is obtained by the proposed temporal maximum filtering method.
 
 
 
 

BBR-S: A Low-Latency BBR Modification for Fast-Varying Connections

The new possibilities offered by 5G and beyond networks have led to a change in the focus of congestion control from capacity maximization for web browsing and file transfer to latency-sensitive interactive and real-time services, and consequently to a renaissance of research on the subject, whose most well-known result is Google's Bottleneck Bandwidth and Round-trip propagation time (BBR) algorithm. BBR's promise is to operate at the optimal working point of a connection, with the minimum Round Trip Time (RTT) and full capacity utilization, striking the balance between resource use efficiency and latency performance. However, while it provides significant performance improvements over legacy mechanisms such as Cubic, it can significantly overestimate the capacity of fast-varying mobile connections, leading to unreliable service and large potential swings in the RTT. Our BBR-S algorithm replaces the max filter that causes this overestimation issue with an Adaptive Tobit Kalman Filter (ATKF), an innovation on the Kalman filter that can deal with unknown noise statistics and saturated measurements, achieving a 40% reduction in the average RTT over BBR, which increases to 60% when considering worst-case latency, while maintaining over 95% of the throughput in 4G and 5G networks.

Invariance-Preserving Localized Activation Functions for Graph Neural Networks

Graph signals are signals with an irregular structure that can be described by a graph. Graph neural networks (GNNs) are information processing architectures tailored to these graph signals and made of stacked layers that compose graph convolutional filters with nonlinear activation functions. Graph convolutions endow GNNs with invariance to permutations of the graph nodes' labels. In this paper, we consider the design of trainable nonlinear activation functions that take into consideration the structure of the graph. This is accomplished by using graph median filters and graph max filters, which mimic linear graph convolutions and are shown to retain the permutation invariance of GNNs. We also discuss modifications to the backpropagation algorithm necessary to train local activation functions. The advantages of localized activation function architectures are demonstrated in four numerical experiments: source localization on synthetic graphs, authorship attribution of 19th century novels, movie recommender systems and scientific article classification. In all cases, localized activation functions are shown to improve model capacity.

Efficient Real-Time R and QRS Detection Method Using a Pair of Derivative Filters and Max Filter for Portable ECG Device

Recently, with the active development of wearable electrocardiogram (ECG) devices such as smart-bands or portable ECG devices, efficient ECG signal processing technology that can be applied in real-time has been actively studied. However, a wearable ECG device is exposed to various noise situations, thereby reducing the reliability of the detected R point or QRS interval. In addition, as early warning techniques in healthcare systems have been studied, real-time ECG signal processing techniques have become very important in wearable ECG devices. In this paper, we propose an efficient real-time R and QRS detection method using two kinds of first-order derivative filters and a max filter to analyze ECG signals measured from wearable ECG devices in real-time. The proposed method detects the R point and QRS interval in units of a sliding window for real-time processing and combines the detected R points in each sliding window. Also, the reliability of the detected R points and RR intervals is examined through noise region analysis using the histogram characteristic of a sample point. The performance of the proposed method was verified by the MIT-BIH database (DB), CYBHi DB and real ECG data measured from the developed wearable ECG patch. The proposed method achieves Se = 99.80%, +P = 99.80%, and DER = 0.36% against MIT-BIH DB. In addition, the proposed method enables accurate R point detection and heart rate variability (HRV) analysis even with noisy ECG signals.

IDENTIFIKASI WAJAH BERBASIS SEGMENTASI WARNA KULIT WAJAH MENGGUNAKAN NAIVE BAYES CLASSIFIER

Face Identification is an important part in digital image processing techniques to determine the size, location and image value. Face detection is a step in the facial recognition system used for personal identification, monitoring system, criminal law, human and computer interaction and so on. This study featuring face detection using Naïve Bayes Classifier with red, green and blue (RGB) model features. This study uses images with variation of facial expression from training data and testing data. The first step is to create a model of facial skin color with RGB model feature which has done normalization process bygrayscaling image, binarying image and filtering image using max filter, then looking for average RGB color of facial skin, followed by building Gaussian distribution showing skin color classification and processed by Naïve method Bayes Classifier (NBC) in determining the classification result.From the test results with a total of 70 test data and a threshold of 0.1, the results of system accuracy reaches 90.25%.

Asymptotically Optimal Algorithms for Running Max and Min Filters on Random Inputs

Given a $d$ -dimensional array of size $n^d$ and an integer $p$ , the running max (or min) filter is the set of maximum (or minimum) elements within a $d$ -dimensional sliding window of edge length $p$ inside the array. This problem is useful in many signal processing applications such as pattern analysis, adaptive signal processing, and morphological analysis. The current best algorithm for computing the one-dimensional (1-D) max (or min) filter, due to the work of [H. Yuan and M. J. Atallah, “Running max/min filters using 1+o(1) comparisons per sample,” IEEE Trans. Pattern Anal. Mach. Intell. , vol. 33, no. 12, pp. 2544–2548, Dec. 2011], uses $1+o(1)$ comparisons per sample in the worst case. As a direct consequence, the $d$ -dimensional max (or min) filter (max and min filters, respectively) can be computed in $d+o(1)$ ( $2d+o(1)$ , respectively) comparisons per sample. In this paper, we first present an algorithm for computing $d$ -dimensional max and min filters simultaneously on i.i.d. inputs that uses $1.5+o(1)$ expected comparisons per sample. This is the first algorithm (on i.i.d. inputs) that gets rid of the dependence on $d$ in the dominating term, with respect to $n$ and $p$ , of the (expected) number of comparisons needed. It is also asymptotically optimal (when $d$ is a fixed constant as $n \rightarrow \infty$ and $p \rightarrow \infty$ ). We also consider the dynamic version of the problem of $d$ -dimensional max and min filters simultaneously on i.i.d. inputs where we want to maintain the filters after changes in the input array. We design a linear-sized data structure that stores precomputed information for efficient update using $O(p^{d-1}\log _2 p)$ expected comparisons per update.

Novel, low power, nonlinear dilatation and erosion filters realized in the CMOS technology

In this paper we propose novel, binary-tree, asynchronous, nonlinear filters suitable for signal processing realized at the transistor level. Two versions of the filter have been proposed, namely the dilatation (Max) and the erosion (Min) one. In the proposed circuits an input signal (current) is sampled in a delay line, controlled by a multiphase clock. In the subsequent stage particular samples are converted to 1-bit digital signals with delays proportional to the values of these samples. In the last step the delays are compared in digital binary-tree structure in order to find either the Min or the Max value, depending on which filter is used. Both circuits have been simulated in the TSMC CMOS 0.18?m technology. To make the results reliable we applied the corner analysis procedure. The circuits were tested for temperatures ranging from -40 to 120?C, for different transistor models and supply voltages. The circuits offer a precision of about 99% at a typical detection time of 20 ns (for the Max filter) and 100 ns for the Min filter (the worst case scenario). The energy consumed per one input during a single calculation cycle equals 0.32 and 1.57 pJ, for the Max and Min filters, respectively.

Automatic Analysis of Smoothing Techniques by Simulation Model Based Real-Time System for Processing 3D Human Faces

The pivotal research work that has been carried out and described in this literature acknowledges the importance of various smoothing techniques for processing 3D human faces from 2.5D range face images. The smoothing techniques have been developed and implemented using MATLAB-Simulink for real time processing in embedded system. In addition, the significance of smoothed 2.5D range image over original face range image has been discovered as well as its time complexity has also been reported with array of experiments. The variations in time complexities are also accomplished using different optimization levels and execution modes. A set of filtering techniques such as, Max filter, Min filter, Median filter, Mean filter, Mid-point filter and Gaussian filter, have been designed and illustrated using Simulink model. The model takes depth face image (i.e. the range face image) as input in real time and presents the improvement over original face images. In the design flow, the performance of every block has also been characterized by range face images from Frav3D, GavabDB, and Bosphorus databases. In the experimental section of this research article, an array of performance analysis for these smoothing techniques with variation of frameworks is explained.

基于人类视觉系统的动态直方图均衡算法<br>Dynamic Histogram Equalization Algorithm Based on Human Visual System

本文提出一种自适应图像增强算法。算法首先用最大值滤波和指数函数滤波平滑直方图，直方图局部最小值为波谷位置，波谷位置把输入图像动态范围分割为各个灰度区域。通过把各灰度区域适当映射到输出灰度区域，获得对比度增强。映射函数根据人类视觉特点进行设计，与灰度区域内均值，标准差及像素数目相关。实验结果显示本算法比其他几个算法达到了更好或相当的对比度增强效果。本算法无需参数调整即能适应各种类型图像，处理速度满足实时系统要求。 In this paper, we propose an adaptive image equalization algorithm that automatically enhances the contrast in an input image. The histogram is firstly smoothed through the max filter and exponential function filter. The troughs of the histogram, which are the local min positions, are used to partition the dynamic range of the image into gray-level intervals. The contrast equalized image is generated by transforming the pixels’ gray-levels in each input interval to the appropriate output gray-level interval according to the mean value, standard deviation and the cumulative distribution function of the input interval, based on human visual system. Experimental results show that the proposed algorithm produces better or comparably enhanced images than several state-of-the-art algorithms. The proposed algorithm is free of parameter setting and can be applied to a wide range of image types. The algorithm also can be used in real-time system.

A hardware friendly algorithm for action recognition using spatio-temporal motion-field patches

A VLSI-hardware-friendly action recognition algorithm using spatio-temporal motion-field patches has been developed. The system employs a hierarchical structure so that the robust recognition can be achieved gradually. At the lower level, motion fields representing local features such as speed and direction are directly calculated from video sequences and further blurred by max filters. At the higher level, a collection of so-called prototype patches are used to recognize query actions by comparing local features in the query videos with those prototypes. In addition, in order to design a system for real-time performance, we intentionally simplify all the calculations into summation operations or boolean operations so that the algorithm can be directly implemented on ultra high speed VLSI chips without much effort. Finally, We tested our system on a gesture perception database as well as widely used action recognition database, and promising recognition performance has been demonstrated.

Running Max/Min Filters Using 1+o(1) Comparisons per Sample

A running max (or min) filter asks for the maximum or (minimum) elements within a fixed-length sliding window. The previous best deterministic algorithm (developed by Gil and Kimmel, and refined by Coltuc) can compute the 1D max filter using 1.5+o(1) comparisons per sample in the worst case. The best known algorithm for independent and identically distributed input uses 1.25+o(1) expected comparisons per sample(by Gil and Kimmel). In this work, we show that the number of comparisons can be reduced to 1+o(1) comparisons per sample in the worst case. As a consequence of the new max/min filters, the opening (or closing) filter can also be computed using 1+o(1) comparisons per sample in the worst case, where the previous best work requires 1.5+o(1) comparisons per sample (by Gil and Kimmel); and computing the max and min filters simultaneously can be done in 2+o(1) comparisons per sample in the worst case, where the previous best work (by Lemire) requires 3 comparisons per sample. Our improvements over the previous work are asymptotic, that is, the number of comparisons is reduced only when the window size is large.

WE-C-351-04: 4DCT Motion Estimation and Modeling

Purpose: To develop a comprehensive high accuracy procedure for computing respiratory motion from 4D‐CT image datasets. The estimated motion field is applied to model and predict respiratory behavior at different breathing states. Method and Materials: The 4D‐CT image data consisted of 16‐slice CT volume segments acquired in cine mode. We used the optical flow deformable image registration algorithm to register the image segments to a common reference 3D‐CT volume. Before registration, the segments were optimally aligned to the reference volume according to the measured tidal volumes and the positions of the diaphragm apex in the inhaled and exhaled phases. Image registration was applied using a multiresolution approach and a feature‐preserving image down‐sampling filter, the max filter, to achieve faster computation speed and better registration accuracy. Computed backward motion fields were inverted to obtain the forward motion fields. Registration accuracy was validated using anatomical landmarks and a digital phantom. The motion fields were fit using 5D (spatial 3D + tidal volume + air flow rate) motion models independently applied to the forward and inverse motion vector maps. The forward model characterized how the tissue moved, and the inverse model characterized how the CTimage density changed with respect to the tidal volume and the air flow rate. Target modeling errors (TME), modeling errors (ME) and modeling prediction errors (MPE) were computed to evaluate these 5D models. Results: The registration error was less than 1.1±0.8 mm for lung tissue. For the forward model, TME = 0.6±0.4 mm, ME and MPE were both 0.3±0.5 mm. For the inverse model, TME = 1.1±0.6 mm, ME = 0.5±0.4 mm and MPE = 0.4±0.5 mm. Conclusion: Our procedure computes 4D respiration motion with high accuracy. Both 5D models could be utilized in multiple radiation oncology applications, including tumor motion tracking and 4D treatment planning.

An Application of LiDAR in a Double-Sample Forest Inventory

Abstract Multireturn LiDAR data (2-m posting) were used in a double-sample forest inventory in central Idaho. Twenty-four 15-plot (0.2 ac) strips were established with a real-time Differential Global Positioning System. Tree dbh and height were measured on every 5th plot. Volume and basal area were computed for eight encountered species. LiDAR trees were selected with a focal max filter and height computed as the z-difference between interpolated canopy and DEM surfaces. LiDAR-derived trees/ac, height, and dbh had mean differences of −4.4 trees, −10.7 ft, and −1.01 in. from ground values. Four dbh-height models were fitted. Predicted dbh was used to compute LiDAR estimates of basal area and volume on 360 Phase 1 plots. Phase 2 LiDAR estimates on 60 plots were computed by randomly assigning heights to species classes using a 500-iteration Monte Carlo simulation. Regression estimators for Phase 2 ground and LiDAR ft3 and ft2 were computed by single and composite species. Phase 1 estimates were partitioned to obtain species volumes. The regression estimate of composite volume was partitioned by percent species distribution of trees, basal area, and volume. There was no statistical difference between individual and partitioned composite species estimates. Sampling error was ±11.5% on a mean volume estimate of 1,246 ft3/ac with standard error ±72.98 ft3/ac. West. J. Appl. For. 19(2):95–101.

Efficient dilation, erosion, opening, and closing algorithms

We propose an efficient and deterministic algorithm for computing the one-dimensional dilation and erosion (max and min) sliding window filters. For a p-element sliding window, our algorithm computes the 1D filter using 1.5 + o(1) comparisons per sample point. Our algorithm constitutes a deterministic improvement over the best previously known such algorithm, independently developed by van Herk (1992) and by Gil and Werman (1993) (the HGW algorithm). Also, the results presented in this paper constitute an improvement over the Gevorkian et al. (1997) (GAA) variant of the HGW algorithm. The improvement over the GAA variant is also in the computation model. The GAA algorithm makes the assumption that the input is independently and identically distributed (the i.i.d. assumption), whereas our main result is deterministic. We also deal with the problem of computing the dilation and erosion filters simultaneously, as required, e.g., for computing the unbiased morphological edge. In the case of i.i.d. inputs, we show that this simultaneous computation can be done more efficiently then separately computing each. We then turn to the opening filter, defined as the application of the min filter to the max filter and give an efficient algorithm for its computation. Specifically, this algorithm is only slightly slower than the computation of just the max filter. The improved algorithms are readily generalized to two dimensions (for a rectangular window), as well as to any higher finite dimension (for a hyperbox window), with the number of comparisons per window remaining constant. For the sake of concreteness, we also make a few comments on implementation considerations in a contemporary programming language.

Apoptosis in leucodepleted packed red blood cells.

Packed red blood cells (pRBCs) contain apoptotic white cells. We studied apoptotic cells in pRBCs after filtration and at various time-points during storage. To maintain the same subset of cells, seven pRBC units were pooled in a single bag and divided equally into seven aliquots. Two series of five experiments were performed: in the first we utilized the Biofil R01 Max filter, and in the second the Pall BPF4 filter was used. One aliquot was immediately leucodepleted while the others were stored at 4 degrees C and filtered on days 3, 7, 10, 14, 21 and 42 of storage. The postfiltration leucocyte counts and apoptotic evaluations were performed by using the Nageotte chamber and flow cytometry. The absolute number of residual leucocytes was always less than 0.5 x 106 in each experiment. Nageotte chamber counts showed a greater number of white blood cells than flow cytometry during the 42 days of storage. On day 0, the percentage of apoptotic cells in non-leucodepleted pRBCs was 1.1 +/- 0.4 and 1.2 +/- 0.4, while in filtered pRBCs it was high from day 0, at 53.5 +/- 16.3 and 52 +/- 18.5, respectively, with Biofil and Pall filters. On day 10 of storage, apoptotic cells reached a percentage of 42.5 +/- 15.8 and 41.6 +/- 18.6 in non-leucodepleted pRBCs, while in filtered units an average value of approximately 90% was found with both filters. The percentage of apoptotic cells was higher in leucodepleted than in non-leucodepleted pRBCs. After filtration, the degree of apoptosis was already high on day 0, and reached a mean of approximately 90% by day 10. The difference in residual WBC counts between the Nageotte chamber and flow cytometry could be related to the presence of a high percentage of apoptotic cells in filtered blood components, and to the method used to distinguish viable from apoptotic cells.

Programmable 1-D rank filter of O(1) time complexity

An efficient architecture and circuit implementation for programmable rank filtering is presented. The circuit ranks a one-dimensional signal in an amount of time independent of the number of signal values and the rank number. The operation is based on one MIN and one MAX filter, and can be efficiently implemented using winner-take-all circuits of O(1) time complexity and O(n) hardware complexity. SPICE simulations and experimental results from a fabricated CMOS chip are included.

Improving Gil-Werman algorithm for running min and max filters

The current best bound on the number of comparison operations needed to compute the running maximum or minimum over a p-element sliding data window is approximately three comparisons per output sample. This bound is probabilistic for some algorithms and is derived for their complexities on the average for independent, identically distributed (i.i.d.) input signals. The worst-case complexities of these algorithms are O(p). The worst-case complexity C/sub r/=3 -4/p comparisons per output sample for 1D signals is achieved in the Gil-Werman algorithm (1993). In this correspondence we propose a modification of the Gil-Werman algorithm with the same worst-case complexity but with a lower average complexity. A theoretical analysis shows that using the proposed modification the complexities of sliding max or min 1D and 2D filters over i.i.d. signals are reduced to C/sub 1/=2.5-3.5/p+1/p/sup 2/ and C/sub 2/=5-7/p+2/p/sup 2/ comparisons per output sample on the average, respectively. Simulations confirm the theoretical results. Moreover, experiments show that even for highly correlated data, namely, for real images the behavior of the algorithm remains the same as for i.i.d. signals.

Computing 2-D min, median, and max filters

Fast algorithms for computing min, median, max, or any other order statistic filter transforms are described. The algorithms take constant time per pixel to compute min or max filters and polylog time per pixel, in the size of the filter, to compute the median filter. A logarithmic time per pixel lower bound for the computation of the median filter is shown.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Rank filters in digital image processing

Rank filters operating on images assign the k th value of the gray levels from the window consisting of M pixels arranged according to their value to the center point of the window. The special cases k = 1, k = M (MIN and MAX filter) and k = ( M + 1)/2 (medium filter), which have already been applied in image processing, are investigated in systematic connection with all rank filters. Some of their properties can be formulated analytically. They commute with monotonic transforms of the gray scale. In the one-dimensional case—also valid for line-like structures in images—the output functions of monotonic input functions can be calculated directly. The alternating application of MIN and MAX filters leads, if repeated more than once, to the same result as a single application. The application of the rank filters to a set of test images shows that there is no simple way to describe their action on the spectrum by means of a transfer or autocorrelation function. In particular the smoothing of the median filter cannot be described in terms of a low-pass filter, but rather by the reduction of the mean local variance. As shown on real and statistical model images, rank filters smooth less than linear filters, but preserve edges.