Merge pull request #27153 from 03kiko:fix-videowriter-writing-colorless-images-26276

fix #26276: cv::VideoWriter fails writing colorless images #27153

When writing grayscale images (`isColor=false`), `cv::VideoWriter` failed as FFmpeg backend requires input frames to be in a grayscale format. Unlike other backends, FFmpeg doesn't perform this conversion internally and expects the input to be pre-converted. To fix this, I inserted a check in the `CvVideoWriter_FFMPEG_proxy::write` to convert input frames to grayscale when the input has more than 1 channel. If this is true, then the input is converted to a gray image using `cv::cvtColor` (with `cv::COLOR_BGR2GRAY`).
Additionally, as suggested in the issue comments, I have correctly propagated the return value of `CvVideoWriter_FFMPEG::writeFrame` back to the `CvVideoWriter_FFMPEG_proxy::write`. This return value wasn't being used, and `writeFrame` was always returning false since the FFmeg's return code `AVERROR(EAGAIN)` was mistakenly being treated as an error. Now it's handled as a signal for additional input (current input was successfully written, and a new frame should be sent. [See FFmpeg documentation for  `avcodec_receive_packet`](https://ffmpeg.org/doxygen/6.1/group__lavc__decoding.html)). A warning is displayed if  `CvVideoWriter_FFMPEG::writeFrame` returns false. Alternatively, this could be propagated back up to the user, making cv::VideoWriter::write a boolean.
Finally, I added a test case to verify if the grayscale conversion is being done correctly. 

Fixes #26276

### Pull Request Readiness Checklist

See details at https://github.com/opencv/opencv/wiki/How_to_contribute#making-a-good-pull-request

- [x] I agree to contribute to the project under Apache 2 License.
- [x] To the best of my knowledge, the proposed patch is not based on a code under GPL or another license that is incompatible with OpenCV
- [x] The PR is proposed to the proper branch
- [x] There is a reference to the original bug report and related work
- [ ] There is accuracy test, performance test and test data in opencv_extra repository, if applicable
      Patch to opencv_extra has the same branch name.
- [ ] The feature is well documented and sample code can be built with the project CMake

modules/videoio/src/cap_ffmpeg.cpp

@@ -194,7 +194,8 @@ public:
             }
         }
 
-        icvWriteFrame_FFMPEG_p(ffmpegWriter, (const uchar*)image.getMat().ptr(), (int)image.step(), image.cols(), image.rows(), image.channels(), 0);
+        if (!icvWriteFrame_FFMPEG_p(ffmpegWriter, (const uchar*)image.getMat().ptr(), (int)image.step(), image.cols(), image.rows(), image.channels(), 0))
+            CV_LOG_WARNING(NULL, "FFmpeg: Failed to write frame");
     }
     virtual bool open( const cv::String& filename, int fourcc, double fps, cv::Size frameSize, const VideoWriterParameters& params )
     {

modules/videoio/src/cap_ffmpeg_impl.hpp

@@ -2525,11 +2525,13 @@ bool CvVideoWriter_FFMPEG::writeFrame( const unsigned char* data, int step, int
     // check parameters
     if (input_pix_fmt == AV_PIX_FMT_BGR24) {
         if (cn != 3) {
+            CV_LOG_WARNING(NULL, "write frame skipped - expected 3 channels but got " << cn);
             return false;
         }
     }
     else if (input_pix_fmt == AV_PIX_FMT_GRAY8 || input_pix_fmt == AV_PIX_FMT_GRAY16LE) {
         if (cn != 1) {
+            CV_LOG_WARNING(NULL, "write frame skipped - expected 1 channel but got " << cn);
             return false;
         }
     }
@@ -2640,14 +2642,16 @@ bool CvVideoWriter_FFMPEG::writeFrame( const unsigned char* data, int step, int
         }
         hw_frame->pts = frame_idx;
         int ret_write = icv_av_write_frame_FFMPEG(oc, video_st, context, outbuf, outbuf_size, hw_frame, frame_idx);
-        ret = ret_write >= 0 ? true : false;
+        // AVERROR(EAGAIN): continue sending input, not an error
+        ret = (ret_write >= 0 || ret_write == AVERROR(EAGAIN));
         av_frame_free(&hw_frame);
     } else
 #endif
     {
         picture->pts = frame_idx;
         int ret_write = icv_av_write_frame_FFMPEG(oc, video_st, context, outbuf, outbuf_size, picture, frame_idx);
-        ret = ret_write >= 0 ? true : false;
+        // AVERROR(EAGAIN): continue sending input, not an error
+        ret = (ret_write >= 0 || ret_write == AVERROR(EAGAIN));
     }
 
     frame_idx++;

modules/videoio/src/cap_gstreamer.cpp

@@ -2699,7 +2699,7 @@ void CvVideoWriter_GStreamer::write(InputArray image)
     }
     else if (input_pix_fmt == GST_VIDEO_FORMAT_GRAY16_LE) {
         if (image.type() != CV_16UC1) {
-            CV_WARN("write frame skipped - expected CV_16UC3");
+            CV_WARN("write frame skipped - expected CV_16UC1");
             return;
         }
     }