基于欧拉法求解类流体颗粒位置与取向控制方程的技术咨询

问题背景 #

我需要推导传送带输送的这类颗粒（整体表现出流体特性）的位置场$(x,y,t)$与取向场$\theta(x,y,t)$的控制方程。

尝试过的方法及问题 #

• 最初采用拉格朗日分析方法，需要识别每个颗粒的位置$(X_i)$和相对水平方向的取向角$\theta_i$，但遇到了严重的图像分割问题：
  • 使用MATLAB编写了基于HSV阈值的分割代码，尝试分割颗粒，但结果显示颗粒形成大块团聚区域，无法区分单个颗粒；
  • 用Python的OpenCV模块尝试分割，效果更差。

所用MATLAB代码 #

clear
function [BW,maskedRGBImage] = mymask(RGB)
%createMask  Threshold RGB image using auto-generated code from colorThresholder app.
%  [BW,MASKEDRGBIMAGE] = createMask(RGB) thresholds image RGB using
%  auto-generated code from the colorThresholder app. The colorspace and
%  range for each channel of the colorspace were set within the app. The
%  segmentation mask is returned in BW, and a composite of the mask and
%  original RGB images is returned in maskedRGBImage.
% Auto-generated by colorThresholder app on 01-Apr-2024
%------------------------------------------------------
% Convert RGB image to chosen color space
I = rgb2hsv(RGB);
% Define thresholds for channel 1 based on histogram settings
channel1Min = 0.009;
channel1Max = 0.112;
% Define thresholds for channel 2 based on histogram settings
channel2Min = 0.103;
channel2Max = 0.275;
% Define thresholds for channel 3 based on histogram settings
channel3Min = 0.347;
channel3Max = 0.687;
% Create mask based on chosen histogram thresholds
sliderBW = (I(:,:,1) >= channel1Min ) & (I(:,:,1) <= channel1Max) & ...
    (I(:,:,2) >= channel2Min ) & (I(:,:,2) <= channel2Max) & ...
    (I(:,:,3) >= channel3Min ) & (I(:,:,3) <= channel3Max);
BW = sliderBW;
% Initialize output masked image based on input image.
maskedRGBImage = RGB;
% Set background pixels where BW is false to zero.
maskedRGBImage(repmat(~BW,[1 1 3])) = 0;
end
inpict = imread('test.png');
mk = mymask(inpict); % create a mask using global thresholds
mk = bwareaopen(mk,100); % get rid of a thousand tiny specks
S = regionprops(mk,'area');
CT = hsv(numel(S));
CT(2:2:end,:) = flipud(CT(2:2:end,:));
% the result is one giant conglomerate blob
% and several smaller conglomerate blobs
alpha = 0.8;
outpict = labeloverlay(inpict,bwlabel(mk), ...
    'transparency',1-alpha,'colormap',CT);
imshow(outpict,'border','tight')

分割结果 #

MATLAB的分割结果显示画面中存在一个大型团聚块和若干小型团聚块，完全无法区分出单个颗粒，导致拉格朗日法无法实施。

核心疑问 #

由于逐颗粒随时间追踪的难度极大，请问如何采用欧拉分析方法推导这类颗粒的控制方程，或者获取对应的场参数？

内容的提问来源于stack exchange，提问作者LOL Ciskram