Detection of small circles with OpenCV (poor image quality)

I am trying to find four points that you can see in the center of this picture: This one is converted to png, I actually use the ppm format (after converting from the original output from the camera). The actual processed image is available here.

I am new to opencv and therefore am having a huge problem finding these points. Here is my best result:

As you can see, I found 3 points, but besides this, many other things in the picture are recognized as circles.

And here is the code:

    IplImage* img;
    if((img = cvLoadImage( "photos/img-000012.ppm", 1)) == 0 )
    {
        perror("cvLoadImage");
        return 1;
    }
    cvNamedWindow( "Image view", 1 );
    cvShowImage( "Image view", img );
//  cvWaitKey(0);

    IplImage* gray = cvCreateImage( cvGetSize(img), 8, 1 ); // allocate a 1 channel byte image
    CvMemStorage* storage = cvCreateMemStorage(0);
    cvCvtColor( img, gray, CV_BGR2GRAY );
    cvShowImage( "Image view", gray );
//  cvWaitKey(0);

    cvSmooth( gray, gray, CV_GAUSSIAN, 3, 3, 0, 0 );
    cvShowImage( "Image view", gray );
    cvWaitKey(0);

    CvSeq* circles = cvHoughCircles(gray, storage, CV_HOUGH_GRADIENT,
            4,      // inverse ratio of the accumulator resolution
            1,      // minimum distance between circle centres
            100,    // higher threshold value for Canny
            20,     // accumulator threshold for the circle centers; smaller->more false circles
            1,  // minimum radius
            10 );   // maximum radius

    printf("circles == %d\n", circles->total);
    int i;
    for (i = 0; i < circles->total; i++) {
        float *p = (float*)cvGetSeqElem(circles, i);
        CvPoint center = cvPoint(cvRound(p[0]),cvRound(p[1]));
        CvScalar val = cvGet2D(gray, center.y, center.x);
        if (val.val[0] < 1) continue;
        printf("%d %d %d\n", cvRound(p[0]),cvRound(p[1]), cvRound(p[2]));
        cvCircle(img,  center, cvRound(p[2]),             CV_RGB(0,255,0), 1, CV_AA, 0);
    }
    cvShowImage( "Image view", img );
    cvWaitKey(0);

Do you have any ideas how to do this? I would be very grateful. I think it’s easy enough for the human eye to spot points, so I hope I can detect them using a computer.