根据输入的灰度图像，分别计算图像的均值、方差等统计特征，并计算图像的直方图特征并以图形方式显示图像的直方图（用C或C++语言实现）。

以下是一个使用C++语言实现的示例程序，可以计算灰度图像的均值、方差和直方图特征，并以图形方式显示直方图：

#include <iostream>
#include <fstream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <opencv2/opencv.hpp>

using namespace std;
using namespace cv;

double get_mean(const Mat& img) {
    double sum = 0;
    for (int i = 0; i < img.rows; i++) {
        for (int j = 0; j < img.cols; j++) {
            sum += img.at<uint8_t>(i, j);
        }
    }
    return sum / (img.rows * img.cols);
}

double get_variance(const Mat& img, double mean) {
    double sum = 0;
    for (int i = 0; i < img.rows; i++) {
        for (int j = 0; j < img.cols; j++) {
            double diff = img.at<uint8_t>(i, j) - mean;
            sum += diff * diff;
        }
    }
    return sum / (img.rows * img.cols - 1);
}

vector<int> get_histogram(const Mat& img) {
    vector<int> hist(256, 0);
    for (int i = 0; i < img.rows; i++) {
        for (int j = 0; j < img.cols; j++) {
            hist[img.at<uint8_t>(i, j)]++;
        }
    }
    return hist;
}

void show_histogram(const vector<int>& hist) {
    int max_count = *max_element(hist.begin(), hist.end());
    int height = 256;
    int width = hist.size() * 2;
    Mat image(height, width, CV_8UC1, Scalar(255));
    for (int i = 0; i < hist.size(); i++) {
        int count = hist[i];
        int x1 = i * 2;
        int y1 = height;
        int x2 = (i + 1) * 2 - 1;
        int y2 = height - count * height / max_count;
        rectangle(image, Point(x1, y1), Point(x2, y2), Scalar(0), -1);
    }
    imshow("Histogram", image);
}

int main(int argc, char** argv) {
    if (argc < 2) {
        cout << "Usage: " << argv[0] << " <image_file>" << endl;
        return 0;
    }

    Mat image = imread(argv[1], IMREAD_GRAYSCALE);
    if (image.empty()) {
        cout << "Failed to open image file " << argv[1] << endl;
        return 0;
    }

    double mean = get_mean(image);
    double variance = get_variance(image, mean);
    vector<int> hist = get_histogram(image);

    cout << "Mean: " << mean << endl;
    cout << "Variance: " << variance << endl;

    namedWindow("Image", WINDOW_NORMAL);
    imshow("Image", image);

    namedWindow("Histogram", WINDOW_NORMAL);
    show_histogram(hist);

    waitKey(0);

    return 0;
}

这个程序使用OpenCV库来读取图像文件和显示图像和直方图。可以通过命令行参数指定要处理的图像文件。程序首先计算图像的均值和方差，并输出到控制台上。然后计算图像的直方图，将直方图特征显示在一个图形窗口中。