He seguido algunos ejemplos sobre SO de cómo recuperar una imagen de la cámara o Gallary. La parte de la cámara funciona, pero la parte de gallary no funciona. El código parece muy difícil de entender para mí, así que no sé qué cuidar exactamente.

También tengo los permisos necesarios en mi manifiesto.

Aquí hay un video del problema:https://www.youtube.com/watch?v=OOoY1y4W86w

ImagePicker (View V), intento / elección, archivos, URIS

public void ImagePicker(View v) {

    if (Environment.MEDIA_MOUNTED.equals(Environment.getExternalStorageState())) {
        if (PackageManager.PERMISSION_GRANTED == ActivityCompat.checkSelfPermission(this, Manifest.permission.WRITE_EXTERNAL_STORAGE) && PackageManager.PERMISSION_GRANTED == ActivityCompat.checkSelfPermission(this, Manifest.permission.READ_EXTERNAL_STORAGE)) {

            final File rootdir = new File(Environment.getExternalStorageDirectory() + File.separator + "TravelDiary" + File.separator);
            rootdir.mkdirs();
            final String filename = "img_" + System.currentTimeMillis() + ".jpg";
            final File sdImageMainDirecotry = new File(rootdir, filename);
            outputFileUri = Uri.fromFile(sdImageMainDirecotry);
            Log.d("TAG", "IM HERE 1");

            //camera
            final List<Intent> cameraIntents = new ArrayList<>();
            final Intent CameraCaptureIntent = new Intent(MediaStore.ACTION_IMAGE_CAPTURE);
            final PackageManager packageManager = getPackageManager();
            final List<ResolveInfo> listcam = packageManager.queryIntentActivities(CameraCaptureIntent, 0);
            Log.d("TAG", "IM HERE 2");


            for (ResolveInfo res : listcam) {

                final String packageName = res.activityInfo.packageName;
                final Intent intent = new Intent(CameraCaptureIntent);
                intent.setComponent(new ComponentName(res.activityInfo.packageName, res.activityInfo.name));
                intent.setPackage(packageName);
                intent.putExtra(MediaStore.EXTRA_OUTPUT, outputFileUri);
                cameraIntents.add(intent);
                Log.d("TAG", "IM HERE 3");
            }


            //Gallary
            final Intent imageChooser = new Intent();
            imageChooser.setType("image/*");
            imageChooser.setAction(Intent.ACTION_GET_CONTENT);


            // Chooser of filesystem options.
            final Intent chooserIntent = Intent.createChooser(imageChooser, "Select Source");

            // Add the camera options.

            chooserIntent.putExtra(Intent.EXTRA_INITIAL_INTENTS, cameraIntents.toArray(new Parcelable[cameraIntents.size()]));
            startActivityForResult(chooserIntent, SELECT_FROM_GALLARY);


        } else {
            ActivityCompat.requestPermissions(this, new String[]{Manifest.permission.WRITE_EXTERNAL_STORAGE, Manifest.permission.READ_EXTERNAL_STORAGE}, 1);
        }
    } else {
        Toast.makeText(this, "External storage not available", Toast.LENGTH_SHORT).show();
    }
}

onActivityResult ():

@Override
protected void onActivityResult(int requestCode, int resultCode, Intent data) {
    if (resultCode == RESULT_OK) {
        if (requestCode == SELECT_FROM_GALLARY) {
            final boolean isCamera;
            if (data == null) {
                isCamera = true;
            } else {
                final String action = data.getAction();
                if (action == null) {
                    isCamera = false;
                } else {
                    isCamera = action.equals(MediaStore.ACTION_IMAGE_CAPTURE);
                }
            }

            Uri selectedImageUri;
            if (isCamera) {

                selectedImageUri = outputFileUri;
                BitmapFactory.Options options = new BitmapFactory.Options();
                options.inSampleSize = 8;
                final Bitmap bitmap = BitmapFactory.decodeFile(selectedImageUri.getPath(), options);
                Drawable drawable = new BitmapDrawable(getResources(), bitmap);
                pic.setBackground(drawable);

            } else {
                selectedImageUri = data == null ? null : data.getData();
                Log.d("ImageURI", selectedImageUri.getLastPathSegment());

                BitmapFactory.Options options = new BitmapFactory.Options();
                options.inSampleSize = 8;
                try {

                    InputStream input = getContentResolver().openInputStream(selectedImageUri);
                    final Bitmap bitmap = BitmapFactory.decodeStream(input, null, options);

                    Drawable drawable = new BitmapDrawable(getResources(), bitmap);
                    pic.setBackground(drawable);


                } catch (FileNotFoundException e) {
                    e.printStackTrace();
                }
            }
        }
    }
}