I am trying to implement a motion detection algorithm using state of the art on an esp32camera. This board has 512kB RAM and I don't want to use too much CPU. So I wanted to get a review on what I implemented if there is piece of code which could be optimized. I tried to comment as much as possible and put link on existing code I took and reshaped.


I try to implement Lucas-Kanade optical flow.

My code is composed of :

  • conv : full convolution 1D.

  • transpose : rescale the input vector to 0..255 and transpose the equivalent array into a buffer.

  • LK_optical_flow : The main code that perform a 2D convolution with Sobel filters and input images. Then compute optical flow magnitude.


/** Rescale vector to 0..255 and transpose
 * @param[in] src vector from convolution unscaled 
 * @param[out] dst pointer of buffer image*/
template<typename T>
void transpose(std::vector<T> src, uint8_t *dst, const int w, const int h) {    
    auto max = *std::max_element(src.begin(), src.end());
    auto min = *std::min_element(src.begin(), src.end());
    for(int n = 0; n< w * h; n++) {
        const int i = n / h;
        const int j = n % h;
        dst[n] = (uint8_t)(src[w * j + i] - min) * 255.0 / max;

/** convolution 1D between flattened image and strel
 * from : https://stackoverflow.com/questions/24518989/how-to-perform-1-dimensional-valid-convolution
 * @param f pointer of flattened image buffer
 * @param g structurant element (strel)
 * @return convolved image as vector*/
template<typename T>
std::vector<T> conv(uint8_t *f, const std::vector<T> &g, const int nf) {
    int const ng = g.size();
    int const n  = nf + ng - 1;
    std::vector<T> out(n, T()); 
    for(auto i(0); i < n; ++i) {
        int const jmn = (i >= ng - 1)? i - (ng - 1) : 0;
        int const jmx = (i <  nf - 1)? i            : nf - 1;
        for(auto j(jmn); j <= jmx; ++j) 
            out[i] += (f[j] * g[i - j]);
    out.erase(out.begin(), out.begin() + ng / 2 + 1);  // remove edge due to full convolution
    return out;

/// Optical flow Lucas-Kanade
/** Implement LK optical flow source from wiki:
 * https://en.wikipedia.org/wiki/Lucas%E2%80%93Kanade_method
 * @param src1 pointer to grayscale buffer image instant t
 * @param src2 pointer to grayscale buffer image diff Image between t and t+1
 * @param output Magnitude output image in RGB */
void LK_optical_flow(uint8_t *src1, uint8_t *src2, uint8_t *output, int w, int h)
    //Allocate 1D strel
    std::vector<int> Kernel_Dy = {1, 2, 1};
    std::vector<int> Kernel_Dx = {-1, 0, 1};
    std::vector<int> Kernel_Dt = {1, 1, 1};

    //Allocate fy only. Too much memory on the heap.
    std::vector<int> tmp; 
    uint8_t *fx = src1;
    uint8_t *fy = new uint8_t[w * h];
    uint8_t *ft = src2;

    memset(output, 0, w * h * sizeof(uint8_t));
    memcpy(fy, fx, w * h * sizeof(uint8_t));

    // Compute equivalent of 2D convolution decompose of two 1D convolution.
    // Sobel Dx
    tmp = conv(fx, Kernel_Dx, w*h);
    transpose(tmp, fx, w, h);
    tmp = conv(fx, Kernel_Dy, w*h);
    transpose(tmp, fx, w, h);   
    // Sobel Dy
    tmp = conv(fy, Kernel_Dy, w*h);
    transpose(tmp, fy, w, h);
    tmp = conv(fy, Kernel_Dx, w*h);  
    transpose(tmp, fy, w, h);   
    // Dt
    tmp = conv(ft, Kernel_Dt, w*h);
    transpose(tmp, ft, w, h);
    tmp = conv(ft, Kernel_Dt, w*h);  
    transpose(tmp, ft, w, h);   

    std::vector<int>().swap(tmp); // deallocate tmp 

    //TODO: Create a function for all above : Mag = opticalflow(fx, fy, ft, window=3)
    const int window = 3; //half window size
    float AtA[2][2];
    float Atb[2];
    std::vector<unsigned> Mag(w*h);

    // Lucas Kanade optical flow algorithm
    for(int i=window; i<=w-window;++i){
        for(int j=window; j<h-window;++j){
            memset(Atb, 0, sizeof(float) * 2);
            memset(AtA, 0, sizeof(float) * 4);
            for(int m=-window; m<window;++m){
                const unsigned index = (j + m) * w + (i + m);
                const float Ix = (float) fx[index];
                const float Iy = (float) fy[index];
                const float It = (float) ft[index];
                AtA[0][0] += Ix * Ix;
                AtA[1][1] += Iy * Iy;
                AtA[0][1] += Ix * Iy;
                AtA[1][0] = AtA[0][1];
                Atb[0] += - Ix * It;
                Atb[1] += - Iy * It;
            //Compute inverse of 2x2 array AtA: 1/(ad-bc)[[d -b][-c a]]
            const float det = AtA[0][0] * AtA[1][1] - AtA[0][1] * AtA[1][0];
            const float iAtA[2][2] = {
                {AtA[1][1] / det, - AtA[0][1] / det},
                {iAtA[0][1]     , AtA[0][0] / det}
            //Compute optical flow : [Vx Vy] = inv[AtA] . Atb
            const float Vx = iAtA[0][0] * Atb[0] + iAtA[0][1] * Atb[1];
            const float Vy = iAtA[1][0] * Atb[0] + iAtA[1][1] * Atb[1]; 

            Mag[i + j * w] = hypotf(Vx, Vy); //sqrt(Vx²+Vy²)
    delete [] fy;   
    int max = *std::max_element(Mag.begin(), Mag.end());
    if(max == 0) 
    ESP_LOGI(TAG, "maxMag = %i \n", max);

    //compute output which is Mag rescaled nothing interesting here.

My next step would be to complete the TODO comments.


1 Answer 1


transpose() makes a copy of its input

The first parameter of transpose() is passed by value, which means it makes a copy of src every time it is called. Pass it by const reference instead.

Make functions really generic

You made transpose() and conv() templates. However, apart from templating the type of the input vector, the rest is still hardcoded. Consider making it even more generic:

template<typename InputRange, typename OutputIterator>
void transpose(const InputRange& src, OutputIterator dst, std::size_t w, std::size_t h) {
    auto [min, max] = std::minmax_element(std::begin(src), std::end(src));
    auto scale = static_cast<float>(std::numeric_limits<decltype(*dst)>::max())
                 / (*max - *min);

    for (std::size_t i = 0; i < w; ++i) {
        for (std::size_t j = 0; i < h; ++i) {
            *dst++ = (src[w * j + i] - min) * scale;

Now it works for any kind of input and output, and it will scale correctly for the output type. Note that you had a bug in your scaling: you forgot to subtract min from max before dividing.

You can do something similar for conv(). You might even want to do it for LK_optical_flow().

Use std::size_t for sizes, counts and indices

Instead of using int, prefer to use std::size_t for sizes, counts and indices. It's guaranteed to be the right size to be able to handle any size container.

Create a function that combines convolution and transposition

You always call transpose() right after conv(), and you do this six times. It might be better to create a single functions that does the convolution and tranposition in one go.

Create a conv2D() function

Create a function conv2D() that does an in-place two-dimensional convolution. Internally it could still use one-dimensional convolutions and transpositions, but it will simplify the code in LK_optical_flow().

Also, while for larger kernels, a two-dimensional separable convolution is most efficiently done as two one-dimensional convolutions, here you just have a 3x3 convolution kernel. It might be faster to just implement a straightforward two-dimensional convolution, as this avoids the overhead of the transpositions.

Other issues

  • In conv(), why calculate the first ng / 2 + 1 elements if you are going to immediately erase them?
  • Use std::fill_n() and std::copy_n() instead of std::memset() and std::memcpy(). It avoids having to use sizeof.
  • Avoid manual memory management, just use a std::vector<uin8_t> for fy. Note that std::vector has a constructor that can copy data from another container, so you can just write:
    std::vector<uint8_t> fy(src1, src + w * h);
  • Consider passing references to std::vectors to LK_optical_flow(), instead of raw pointers.
  • To deallocate tmp, just make it go out of scope:
        std::vector<int> tmp;
        tmp = conv(…);
    But it's not even necessary if you have a conv2D() function as mentioned above.
  • Use std::hypot() instead of hypotf(). The former has overloads that will automatically use the right floating point size.

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